EP3568345B1 - Method for determining hydrodynamic coefficients in submarines - Google Patents

Description

The invention relates to a method for determining hydrodynamic coefficients in submarines.

During stationary travel of a submarine, in particular the normal force acting on the boat is equal to zero. This is described by the following equation: $$Z_{\ast }^{\prime }+Z_w^{\prime }\cdot \tan \left(\alpha \right)+Z_{\left|w\right|}\cdot \left|\tan \left(\alpha \right)\right|+Z_{w\left|w\right|}^{\prime }\cdot \tan \left(\alpha \right)\cdot \left|\tan \left(\alpha \right)\right|+Z_{\mathit{ww}}^{\prime }\cdot {\tan }^2\left(\alpha \right)+f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot {\delta }_s+Z_{\mathit{\delta b}}^{\prime }\cdot {\delta }_b+\left(f_x\cdot Z_{\mathit{\delta s\eta }}^{\prime }\cdot {\delta }_s+Z_{\mathit{w\eta }}^{\prime }\cdot \tan \left(\alpha \right)+Z_{w\left|w\right|\eta }^{\prime }\cdot \tan \left(\alpha \right)\cdot \left|\tan \left(\alpha \right)\right|\right)\cdot \left(\eta \cdot \mathrm{C.}-1\right)+\frac{\mathrm{W.}\prime -\mathrm{B.}\prime }{u^{\prime 2}}\cdot \cos \left(\theta \right)\cdot \cos \left(\varphi \right)=0$$

The same applies to those with stationary travel on the boat that the applied trim torques are equal to zero. This describes the following equation: $${\mathrm{M.}}_{\ast }^{\prime }+{\mathrm{M.}}_w^{\prime }\cdot \tan \left(\alpha \right)+{\mathrm{M.}}_{\left|w\right|}\cdot \left|\tan \left(\alpha \right)\right|+{\mathrm{M.}}_{w\left|w\right|}^{\prime }\cdot \tan \left(\alpha \right)\cdot \left|\tan \left(\alpha \right)\right|+{\mathrm{M.}}_{\mathit{ww}}^{\prime }\cdot {\tan }^2\left(\alpha \right)+f_x\cdot {\mathrm{M.}}_{\mathit{\delta s}}^{\prime }\cdot {\delta }_s+{\mathrm{M.}}_{\mathit{\delta b}}^{\prime }\cdot {\delta }_b+\left(f_x\cdot {\mathrm{M.}}_{\mathit{\delta s\eta }}^{\prime }\cdot {\delta }_s+{\mathrm{M.}}_{\mathit{w\eta }}^{\prime }\cdot \tan \left(\alpha \right)+{\mathrm{M.}}_{w\left|w\right|\eta }^{\prime }\cdot \tan \left(\alpha \right)\cdot \left|\tan \left(\alpha \right)\right|\right)\cdot \left(\eta \cdot \mathrm{C.}-1\right)+\frac{x_G^{\prime }\cdot \mathrm{W.}\prime -x_{\mathrm{B.}}^{\prime }\cdot \mathrm{B.}\prime }{u^{\prime 2}}\cdot \cos \left(\theta \right)\cdot \cos \left(\varphi \right)+\frac{x_G^{\prime }\cdot \mathrm{W.}\prime -x_{\mathrm{B.}}^{\prime }\cdot \mathrm{B.}\prime }{u^{\prime 2}}\cdot \sin \left(\theta \right)=0$$

The z-direction is the direction perpendicular to the longitudinal axis of the submarine, with positive values pointing downwards.
The y direction is the direction transverse to the longitudinal axis of the submarine, with positive values pointing to starboard.

W  das Gewicht des Unterseeboots einschließlich gefluteter Freiräume,
$W\prime =\frac{W}{\frac{\rho }{2}\cdot L^2\cdot {\bar{U}}^2}$

  ein dimensionsloser Wert,
B  der Formauftrieb des Unterseeboots,
$B\prime =\frac{B}{\frac{\rho }{2}\cdot L^2\cdot {\bar{U}}^2}$

  ein dimensionsloser Wert,
C  der Ursprung des bootsfesten Koordinatensystems,
L  die Länge des Unterseeboots,
ρ  die Dicht des umgebenden Wassers,
g  die Erdbeschleunigung,
U  die Geschwindigkeit des Unterseeboots bei Fahrt durch das Wasser,
u  die Geschwindigkeitskomponente in x-Richtung,
U   die Geschwindigkeit des Unterseeboots bei stationärer Fahrt durch das Wasser für einen frei wählbaren Referenzfahrtzustand,
u_c   die Propulsionsgeschwindigkeit, welche der Geschwindigkeit u entspricht, die das Boot bei der momentanen Propellerdrehzahl bei Vorausfahrt auf ebenem Kiel mit Nullruderlagen erreichen würde, $u_c^{\prime }=\frac{u}{\bar{U}}$

ein dimensionsloser Wert,
v  die Geschwindigkeitskomponente in y-Richtung quer zum Unterseeboot,
$v\prime =\frac{v}{\bar{U}}$

  ein dimensionsloser Wert,
w  die Geschwindigkeitskomponente in z-Richtung normal zum Unterseeboot,
$w\prime =\frac{w}{\bar{U}}$

  ein dimensionsloser Wert,
Z  die Hydrodynamische Kraft in z-Richtung,
Z _*  der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von u ²,
$Z_{\ast }^{\prime }=\frac{Z_{\ast }}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z_w   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von dem Produkt u · w,
$Z_w^{\prime }=\frac{Z_w}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z _|w|  der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von dem Produkt u · |w|,
$Z_{\left|w\right|}^{\prime }=\frac{Z_{\left|w\right|}}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z _w|w|  der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von $w\cdot \sqrt{v^2+w^2}$

,
$Z_{w\left|w\right|}^{\prime }=\frac{Z_{w\left|w\right|}}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z_ww   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von |w| · $\sqrt{v^2+w^2},$

$Z_{\mathit{ww}}^{\prime }=\frac{Z_{\mathit{ww}}}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z _w|w|η   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von w · $\sqrt{v^2+w^2\cdot }\left(\eta \cdot C-1\right),$

$Z_{w\left|w\right|\eta }^{\prime }=\frac{Z_{w\left|w\right|\eta }}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z_δs   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von u ² · δ_s,
$Z_{\mathit{\delta s}}^{\prime }=\frac{Z_{\mathit{\delta s}}^{\prime }}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z_δb   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von u ² · δ_b,
$Z_{\mathit{\delta b}}^{\prime }=\frac{Z_{\mathit{\delta b}}^{\prime }}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
Z _δsη   der Koeffizient zur Beschreibung der Normalkraft Z als Funktion von u ² · δ_s · (η · C - 1),
$Z_{\mathit{\delta s\eta }}^{\prime }=\frac{Z_{\mathit{\delta s\eta }}^{\prime }}{\frac{\rho }{2}{L}^2}$

  ein dimensionsloser Wert,
M  das hydrodynamische Drehmoment um die y-Achse, auch Stampfmoment genannt,
M _*  der Koeffizient zur Beschreibung des Stampfmoments M,
$M_{\ast }^{\prime }=\frac{M_{\ast }}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M_w   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von u · w,
$M_w^{\prime }=\frac{M_w}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M _|w|  der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von u · |w|,
$M_{\left|w\right|}^{\prime }=\frac{M_{\left|w\right|}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M _w|w|  der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von w · $\sqrt{v^2+w^2},$

$M_{w\left|w\right|}^{\prime }=\frac{M_{w\left|w\right|}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M_ww   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von |w| ·
$M_{\mathit{ww}}^{\prime }=\frac{M_{\mathit{ww}}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M _w|w|η   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von w · $\sqrt{v^2+w^2\cdot }\left(\eta \cdot C-1\right),$

$M_{w\left|w\right|\eta }^{\prime }=\frac{M_{w\left|w\right|\eta }}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M_δs   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von u ² · δ_s,
$M_{\mathit{\delta s}}^{\prime }=\frac{M_{\mathit{\delta s}}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M_δb   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von u ² · δ_b,
$M_{\mathit{\delta b}}^{\prime }=\frac{M_{\mathit{\delta b}}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert,
M_δSη   der Koeffizient zur Beschreibung des Stampfmoments M als Funktion von u ² · δ_s · (η · C - 1),
$M_{\mathit{\delta s\eta }}^{\prime }=\frac{M_{\mathit{\delta s\eta }}}{\frac{\rho }{2}{L}^3}$

  ein dimensionsloser Wert.Where is:
δ _{s is} the aft depth rudder angle,
δ _{b is} the forward depth rudder angle,
α is the angle of attack of the submarine,
β is the drift angle of the submarine,
f _x a factor for rudder, with X rudder f _x = 4, with cross rudder f _x = 1,
η the ratio $\frac{u_c}{u},$

W is the weight of the submarine including flooded clearances,
$\mathrm{W.}\prime =\frac{\mathrm{W.}}{\frac{\rho }{2}\cdot {\mathrm{L.}}^2\cdot {\bar{U}}^2}$

a dimensionless value,
B is the buoyancy of the submarine,
$\mathrm{B.}\prime =\frac{\mathrm{B.}}{\frac{\rho }{2}\cdot {\mathrm{L.}}^2\cdot {\bar{U}}^2}$

a dimensionless value,
C is the origin of the boat-based coordinate system,
L is the length of the submarine,
ρ is the density of the surrounding water,
g is the acceleration due to gravity,
U the speed of the submarine when traveling through the water,
u is the speed component in the x direction,
U the speed of the submarine during stationary travel through the water for a freely selectable reference travel state,
u _{c is} the propulsion speed, which corresponds to the speed u that the boat would achieve at the current propeller speed when traveling ahead on a level keel with zero rudder angles, $u_c^{\prime }=\frac{u}{\bar{U}}$

a dimensionless value,
v is the speed component in the y direction across the submarine,
$v\prime =\frac{v}{\bar{U}}$

a dimensionless value,
w is the speed component in the z direction normal to the submarine,
$w\prime =\frac{w}{\bar{U}}$

a dimensionless value,
Z is the hydrodynamic force in the z direction,
Z _{* is} the coefficient describing the normal force Z as a function of u ² ,
$Z_{\ast }^{\prime }=\frac{Z_{\ast }}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{w is} the coefficient describing the normal force Z as a function of the product u w ,
$Z_w^{\prime }=\frac{Z_w}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{| w |} the coefficient describing the normal force Z as a function of the product u · | w |,
$Z_{\left|w\right|}^{\prime }=\frac{Z_{\left|w\right|}}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{w | w |} the coefficient describing the normal force Z as a function of $w\cdot \sqrt{v^2+w^2}$

,
$Z_{w\left|w\right|}^{\prime }=\frac{Z_{w\left|w\right|}}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{ww is} the coefficient describing the normal force Z as a function of | w | · $\sqrt{v^2+w^2},$

$Z_{\mathit{ww}}^{\prime }=\frac{Z_{\mathit{ww}}}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{w | w | η is} the coefficient to describe the normal force Z as a function of w $\sqrt{v^2+w^2\cdot }\left(\eta \cdot \mathrm{C.}-1\right),$

$Z_{w\left|w\right|\eta }^{\prime }=\frac{Z_{w\left|w\right|\eta }}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{δs is} the coefficient describing the normal force Z as a function of u ² δ _s ,
$Z_{\mathit{\delta s}}^{\prime }=\frac{Z_{\mathit{\delta s}}^{\prime }}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{δb is} the coefficient describing the normal force Z as a function of u ² δ _b ,
$Z_{\mathit{\delta b}}^{\prime }=\frac{Z_{\mathit{\delta b}}^{\prime }}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
Z _{δ s η is} the coefficient describing the normal force Z as a function of u ² δ _s ( η C - 1),
$Z_{\mathit{\delta s\eta }}^{\prime }=\frac{Z_{\mathit{\delta s\eta }}^{\prime }}{\frac{\rho }{2}{\mathrm{L.}}^2}$

a dimensionless value,
M is the hydrodynamic torque around the y- axis, also called pitching torque,
M _{* is} the coefficient describing the pitching moment M ,
${\mathrm{M.}}_{\ast }^{\prime }=\frac{{\mathrm{M.}}_{\ast }}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{w is} the coefficient for describing the pitching moment M as a function of u w,
${\mathrm{M.}}_w^{\prime }=\frac{{\mathrm{M.}}_w}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{| w |} the coefficient for describing the pitching moment M as a function of u · | w |,
${\mathrm{M.}}_{\left|w\right|}^{\prime }=\frac{{\mathrm{M.}}_{\left|w\right|}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{w | w |} the coefficient to describe the pitching moment M as a function of w $\sqrt{v^2+w^2},$

${\mathrm{M.}}_{w\left|w\right|}^{\prime }=\frac{{\mathrm{M.}}_{w\left|w\right|}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{ww is} the coefficient describing the pitching moment M as a function of | w | ·
${\mathrm{M.}}_{\mathit{ww}}^{\prime }=\frac{{\mathrm{M.}}_{\mathit{ww}}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{w | w | η is} the coefficient to describe the pitching moment M as a function of w $\sqrt{v^2+w^2\cdot }\left(\eta \cdot \mathrm{C.}-1\right),$

${\mathrm{M.}}_{w\left|w\right|\eta }^{\prime }=\frac{{\mathrm{M.}}_{w\left|w\right|\eta }}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{δs is} the coefficient for describing the pitching moment M as a function of u ² δ _s ,
${\mathrm{M.}}_{\mathit{\delta s}}^{\prime }=\frac{{\mathrm{M.}}_{\mathit{\delta s}}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{δb is} the coefficient for describing the pitching moment M as a function of u ² δ _b ,
${\mathrm{M.}}_{\mathit{\delta b}}^{\prime }=\frac{{\mathrm{M.}}_{\mathit{\delta b}}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value,
M _{δSη is} the coefficient to describe the pitching moment M as a function of u ² δ _s ( η C - 1),
${\mathrm{M.}}_{\mathit{\delta s\eta }}^{\prime }=\frac{{\mathrm{M.}}_{\mathit{\delta s\eta }}}{\frac{\rho }{2}{\mathrm{L.}}^3}$

a dimensionless value.

These hydrodynamic coefficients can be calculated theoretically or determined experimentally in a model test. However, this is extremely complex and cannot be carried out precisely for the current loading situation of the submarine, so that approximate values have to be used.

The exact knowledge of these parameters allows a precise prediction of the boat behavior. Maneuvers can thus be controlled very precisely if these parameters are known exactly. The hydrodynamic coefficients calculated or determined in a model test are therefore generally too imprecise for a precise prediction of the boat behavior. For this reason, the hydrodynamic coefficients are usually verified or corrected by evaluating large-scale construction tests, although the large-scale construction tests used today only represent complex approximation methods.

The JP S63 43896 A has the purpose of automatically adjusting weighting and trimming. For this purpose, data is recorded with sensors.

From the US 2004/224577 A1 a device for navigational control of a watercraft is known.

The object of the invention is to provide a method with which these hydrodynamic coefficients can be recorded or determined simply and precisely by measuring technology on a real submarine.

This object is achieved by the method for determining hydrodynamic coefficients in submarines with the features specified in claim 1. Advantageous further developments result from the subclaims, the following description and the drawings.

1. a) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei einer ersten ersten Geschwindigkeit und einer ersten ersten Trimmlage,
2. b) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei der ersten ersten Geschwindigkeit und einer zweiten ersten Trimmlage,
3. c) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei einer zweiten ersten Geschwindigkeit und der ersten ersten Trimmlage,
4. d) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei der zweiten ersten Geschwindigkeit und der zweiten ersten Trimmlage,
5. e) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer ersten zweiten Geschwindigkeit und einer ersten vorderen Tiefenruderlage und einer ersten Trimmtankfüllung,
6. f) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der ersten zweiten Geschwindigkeit und einer zweiten vorderen Tiefenruderlage und der ersten Trimmtankfüllung,
7. g) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der ersten zweiten Geschwindigkeit und der ersten vorderen Tiefenruderlage und einer zweiten Trimmtankfüllung,
8. h) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der ersten zweiten Geschwindigkeit und der zweiten vorderen Tiefenruderlage und der zweiten Trimmtankfüllung,
9. i) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer zweiten zweiten Geschwindigkeit und der ersten vorderen Tiefenruderlage und der ersten Trimmtankfüllung,
10. j) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der zweiten zweiten Geschwindigkeit und der zweiten vorderen Tiefenruderlage und der ersten Trimmtankfüllung,
11. k) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der zweiten zweiten Geschwindigkeit und der ersten vorderen Tiefenruderlage und der zweiten Trimmtankfüllung,
12. l) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei der zweiten zweiten Geschwindigkeit und der zweiten vorderen Tiefenruderlage und der zweiten Trimmtankfüllung,
13. m) Ermitteln von hydrodynamischen Koeffizienten aus den in den vorhergehenden Schritten ermittelten Messgrößen,

wobei die Schritte a) bis l) in beliebiger Reihenfolge durchgeführt werden. Der Schritt m) wird nach den Schritten a) bis l) durchgeführt.The method according to the invention for determining hydrodynamic coefficients in submarines with a front down elevator and a rear down elevator has the following steps:

1. a) Acceleration-free travel with a level keel at constant depth and at a first first speed and a first first trim position,
2. b) Acceleration-free travel with a level keel at constant depth and at the first first speed and a second first trim position,
3. c) Acceleration-free travel with a level keel at constant depth and at a second first speed and the first first trim position,
4. d) Acceleration-free travel with a level keel at constant depth and at the second first speed and the second first trim position,
5. e) Acceleration-free travel with an inclined keel at constant depth and at a first second speed and a first forward depth rudder position and a first trim tank filling,
6. f) Acceleration-free travel with an inclined keel at constant depth and at the first second speed and a second forward depth rudder position and the first trim tank filling,
7. g) Acceleration-free travel with an inclined keel at constant depth and at the first second speed and the first forward depth rudder position and a second trim tank filling,
8. h) Acceleration-free travel with an inclined keel at constant depth and at the first second speed and the second forward depth rudder position and the second trim tank filling,
9. i) Acceleration-free travel with an inclined keel at constant depth and at a second, second speed and the first forward depth rudder position and the first trim tank filling,
10. j) Acceleration-free travel with an inclined keel at constant depth and at the second second speed and the second forward depth rudder position and the first trim tank filling,
11. k) Acceleration-free travel with an inclined keel at constant depth and at the second second speed and the first forward depth rudder position and the second trim tank filling,
12. l) acceleration-free travel with an inclined keel at constant depth and at the second second speed and the second forward depth rudder position and the second trim tank filling,
13. m) Determination of hydrodynamic coefficients from the measured variables determined in the previous steps,

wherein steps a) to l) are carried out in any order. Step m) is carried out according to steps a) to l).

The submarine is free-swimming in this procedure. Free floating means that the submarine is not towed or has some other form of connection, for example a submarine model that is attached to a rod. So none work external forces on the submarine, for example a force via a tow rope. When traveling without acceleration, the submarine is therefore force-free, i.e. all forces, acceleration from the propeller, friction, buoyancy from the hull, buoyancy from the rudder, etc., balance each other out. Free swimming thus enables direct and simple determination on a specific submarine and not on a model. As a result, the parameters determined are exact and can be determined individually depending on the state, for example different loads.

Under a flat keel there is in particular a pitch angle θ of the submarine of −1 ° < θ <+ 1 °, preferably of −0.2 ° <θ <+ 0.2 °, particularly preferably of −0.05 ° < θ <+ 0.05 ° to be understood. The pitch angle is the angle between the longitudinal axis of the submarine and the projection of the longitudinal axis of the submarine into the plane and thus reflects the inclination in the z-direction.

Under an inclined keel, a particular pitch angle θ of the submarine is | θ | > 0.5 °, preferably from | θ | > 1 °, particularly preferably from | θ | > 2 ° to be understood.

Acceleration-free travel is understood to mean an operating mode in which the boat moves at a constant speed, with constant being regarded as constant within the scope of the detection accuracy and control accuracy.

Since the journey takes place at a constant depth, the vertical forces, i.e. the gravitational or lift acceleration, compensate each other so that there is no uplift or downforce.

When driving without acceleration, the forces balance each other out. Thus, there is no resulting force acting on the submarine. It is therefore true that the sum of all acting forces is zero. Furthermore, the sum of all force changes between two acceleration-free journeys must also be zero. The absolute speed in the horizontal direction is by definition greater than zero when driving. For technical reasons, very low speeds, in particular less than 2 kn, very particularly less than 1 kn, are not advantageous.

In order to indicate the measured values in a meaningful way, the various first speeds and second speeds are designated with the index i . So i = 1 for the first first Speed and the first second speed and i = 2 for the second first speed and the second second speed.

As a further index, k is used to distinguish the trim and weight conditions. So k = 1 for the first trim position and the first forward elevator position and k = 2 for the second first trim position and the second forward elevator position.

The measured values are evaluated separately for journeys with a flat keel and with a sloping keel.

For example, first of all the measured values for the journeys with a level keel are evaluated.

durch Berechnung von Ausgleichsgeraden ausgewertet. Die Ausgleichsgeraden ergeben als Grenzwerte für u → ∞ die hinteren Tiefenruderwinkel δ_sn und vorderen Tiefenruderwinkel δ_bn für die sogenannte auftrieb- und momentfreie Fahrt. Es werden hierbei nur die Grenzwerte ausgewertet. $${\delta }_{\mathit{ski}}={\delta }_{\mathit{sn}}-\frac{g\cdot L}{u_{\mathit{ki}}^2}\cos \left({\varphi }_{\mathit{ki}}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)\cdot V_{\mathit{CTki}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot V_{\mathit{TTki}}^{\prime }}{f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

$${\delta }_{\mathit{bki}}={\delta }_{\mathit{bn}}+\frac{g\cdot L}{u_{\mathit{ki}}^2}\cos \left({\varphi }_{\mathit{ki}}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta s}}^{\prime }\right)\cdot V_{\mathit{CTki}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot V_{\mathit{TTki}}^{\prime }}{Z_{\mathit{\delta s}}^{\prime }\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

First, the measured values obtained in steps a) to d) are shown as a function of $\frac{1}{u_{\mathit{ki}}^2}$

evaluated by calculating best-fit straight lines. The best-fit straight lines result as limit values for u → ∞ the rear depth rudder angle δ _sn and front depth rudder angle δ _bn for the so-called lift and torque-free ride. Only the limit values are evaluated here. $${\delta }_{\mathit{ski}}={\delta }_{\mathit{sn}}-\frac{G\cdot \mathrm{L.}}{u_{\mathit{ki}}^2}\cos \left({\varphi }_{\mathit{ki}}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)\cdot V_{\mathit{CTki}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot V_{\mathit{TTki}}^{\prime }}{f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

$${\delta }_{\mathit{bki}}={\delta }_{\mathit{bn}}+\frac{G\cdot \mathrm{L.}}{u_{\mathit{ki}}^2}\cos \left({\varphi }_{\mathit{ki}}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta s}}^{\prime }\right)\cdot V_{\mathit{CTki}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot V_{\mathit{TTki}}^{\prime }}{Z_{\mathit{\delta s}}^{\prime }\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

  ein dimensionsloser Wert,
Δx_TT   der positive Abstand des Schwerpunkts vom vorderen zum hinteren Trimmzellenvolumen,
$\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }=\frac{\mathrm{\Delta }{x}_{\mathit{TT}}}{L}$

  ein dimensionsloser Wert,
x_δs   die x-Koordinate des vorderen Tiefenruders,
$x_{\mathit{\delta s}}^{\prime }=\frac{x_{\mathit{\delta s}}}{L}$

  ein dimensionsloser Wert,
x_δb   die x-Koordinate des hinteren Tiefenruders,
$x_{\mathit{\delta b}}^{\prime }=\frac{x_{\mathit{\delta b}}}{L}$

  ein dimensionsloser Wert,
V_CT   das Füllvolumen der Regelzelle,
$V_{\mathit{CT}}^{\prime }=\frac{V_{\mathit{CT}}}{\frac{1}{2}{L}^3}$

  ein dimensionsloser Wert,
V_TT   die Trimmzellenfüllung, wobei das Trimmmoment M_TT =- ρ · Δx_TT · V_TT ist,
$V_{\mathit{TT}}^{\prime }=\frac{V_{\mathit{TT}}}{\frac{1}{2}{L}^3}$

  ein dimensionsloser Wert.Where is:
x _{CT is} the x coordinate of the center of gravity of the control cell,
$x_{\mathit{CT}}^{\prime }=\frac{x_{\mathit{CT}}}{\mathrm{L.}}$

a dimensionless value,
Δx _{TT is} the positive distance of the center of gravity from the front to the rear trim cell volume,
$\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }=\frac{\mathrm{\Delta }{x}_{\mathit{TT}}}{\mathrm{L.}}$

a dimensionless value,
x _δs the x -coordinate of the forward depth rudder,
$x_{\mathit{\delta s}}^{\prime }=\frac{x_{\mathit{\delta s}}}{\mathrm{L.}}$

a dimensionless value,
x _{δb is} the x -coordinate of the rear depth rudder,
$x_{\mathit{\delta b}}^{\prime }=\frac{x_{\mathit{\delta b}}}{\mathrm{L.}}$

a dimensionless value,
V _{CT is} the filling volume of the control cell,
$V_{\mathit{CT}}^{\prime }=\frac{V_{\mathit{CT}}}{\frac{1}{2}{\mathrm{L.}}^3}$

a dimensionless value,
V _{TT is} the trim cell filling, where the trim moment M _TT = - ρ · Δx _TT · V _TT ,
$V_{\mathit{TT}}^{\prime }=\frac{V_{\mathit{TT}}}{\frac{1}{2}{\mathrm{L.}}^3}$

a dimensionless value.

aufgetragen. Die Steigung dieser Geraden ist nicht relevant, entscheidet ist der für null und somit für $u_{\mathit{ki}}^2$

gegen unendlich extrapolierte Grenzwert. Die x-Koordinaten von Trimm- und Regelzellen und Ruderposition sind aus der Bootsgeometrie bekannt.As already stated, the rudder angles are about $\frac{1}{u_{\mathit{ki}}^2}$

applied. The slope of this straight line is not relevant, it is decisive for zero and thus for $u_{\mathit{ki}}^2$

towards infinitely extrapolated limit value. The x-coordinates of trim and control cells and rudder position are known from boat geometry.

und $$\mathrm{\Delta }{\delta }_{\mathit{bi}}\left(u_i\right)={\delta }_{b2i}\left(u_i\right)-{\delta }_{b1i}\left(u_i\right)$$

werden die Werte $$Z_{\mathit{\delta si}}^{\prime }=-\frac{g\cdot L}{2}\left(\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{\mathit{ki}}^2}+\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{2i}^2}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)\cdot \mathrm{\Delta }{V}_{\mathit{CT}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot \mathrm{\Delta }{V}_{\mathit{TT}}^{\prime }}{f_x\cdot \mathrm{\Delta }{\delta }_{\mathit{si}}\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

und $$Z_{\mathit{\delta bi}}^{\prime }=-\frac{g\cdot L}{2}\left(\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{\mathit{ki}}^2}+\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{2i}^2}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta s}}^{\prime }\right)\cdot \mathrm{\Delta }{V}_{\mathit{CT}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot \mathrm{\Delta }{V}_{\mathit{TT}}^{\prime }}{f_x\cdot \mathrm{\Delta }{\delta }_{\mathit{bi}}\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

ermittelt. Die Koeffizienten $Z_{\mathit{\delta s}}^{\prime }$

und $Z_{\mathit{\delta b}}^{\prime }$

ergeben sich daraus als Mittelwerte.By subtracting the values determined from steps a) to d) at different trim and weight states measured rudder angles according to $$\mathrm{\Delta }{\delta }_{\mathit{si}}\left(u_i\right)={\delta }_{s2i}\left(u_i\right)-{\delta }_{s1i}\left(u_i\right)$$

and $$\mathrm{\Delta }{\delta }_{\mathit{bi}}\left(u_i\right)={\delta }_{b2i}\left(u_i\right)-{\delta }_{b1i}\left(u_i\right)$$

become the values $$Z_{\mathit{\delta si}}^{\prime }=-\frac{G\cdot \mathrm{L.}}{2}\left(\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{\mathit{ki}}^2}+\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{2i}^2}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)\cdot \mathrm{\Delta }{V}_{\mathit{CT}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot \mathrm{\Delta }{V}_{\mathit{TT}}^{\prime }}{f_x\cdot \mathrm{\Delta }{\delta }_{\mathit{si}}\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

and $$Z_{\mathit{\delta bi}}^{\prime }=-\frac{G\cdot \mathrm{L.}}{2}\left(\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{\mathit{ki}}^2}+\frac{\cos \left({\varphi }_{\mathit{ki}}\right)}{u_{2i}^2}\right)\frac{\left(x_{\mathit{CT}}^{\prime }-x_{\mathit{\delta s}}^{\prime }\right)\cdot \mathrm{\Delta }{V}_{\mathit{CT}}^{\prime }+\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }\cdot \mathrm{\Delta }{V}_{\mathit{TT}}^{\prime }}{f_x\cdot \mathrm{\Delta }{\delta }_{\mathit{bi}}\cdot \left(x_{\mathit{\delta s}}^{\prime }-x_{\mathit{\delta b}}^{\prime }\right)}$$

determined. The coefficients $Z_{\mathit{\delta s}}^{\prime }$

and $Z_{\mathit{\delta b}}^{\prime }$

result from this as mean values.

$$M_{\mathit{\delta b}}^{\prime }=-Z_{\mathit{\delta b}}^{\prime }\cdot x_{\mathit{\delta b}}^{\prime }$$

sowie: $$Z_{\ast }^{\prime }=-f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot {\delta }_{\mathit{sn}}-Z_{\mathit{\delta b}}^{\prime }\cdot {\delta }_{\mathit{bn}}$$

$$M_{\ast }^{\prime }=-f_x\cdot M_{\mathit{\delta s}}^{\prime }\cdot {\delta }_{\mathit{sn}}-Z_{\mathit{\delta b}}^{\prime }\cdot {\delta }_{\mathit{bn}}$$

$$V_{\mathit{CTki}}^{\prime }=-\frac{u_i^2}{g\cdot L}\cdot \frac{f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot \left({\delta }_{\mathit{ski}}-{\delta }_{\mathit{sn}}\right)+Z_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bki}}-{\delta }_{\mathit{bn}}\right)}{\cos \left({\varphi }_{\mathit{ki}}\right)}$$

$$V_{\mathit{TTki}}^{\prime }=\frac{1}{\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }}\left(\frac{u_i^2}{g\cdot L}\cdot \frac{f_x\cdot M_{\mathit{\delta s}}^{\prime }\cdot \left({\delta }_{\mathit{ski}}-{\delta }_{\mathit{sn}}\right)+M_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bki}}-{\delta }_{\mathit{bn}}\right)}{\cos \left({\varphi }_{\mathit{ki}}\right)}-x_{\mathit{CT}}^{\prime }\cdot V_{\mathit{CTki}}^{\prime }\right)$$

This then gives the coefficients for describing the pitching torque: $${\mathrm{M.}}_{\mathit{\delta s}}^{\prime }=-Z_{\mathit{\delta s}}^{\prime }\cdot x_{\mathit{\delta s}}^{\prime }$$

$${\mathrm{M.}}_{\mathit{\delta b}}^{\prime }=-Z_{\mathit{\delta b}}^{\prime }\cdot x_{\mathit{\delta b}}^{\prime }$$

as: $$Z_{\ast }^{\prime }=-f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot {\delta }_{\mathit{sn}}-Z_{\mathit{\delta b}}^{\prime }\cdot {\delta }_{\mathit{bn}}$$

$${\mathrm{M.}}_{\ast }^{\prime }=-f_x\cdot {\mathrm{M.}}_{\mathit{\delta s}}^{\prime }\cdot {\delta }_{\mathit{sn}}-Z_{\mathit{\delta b}}^{\prime }\cdot {\delta }_{\mathit{bn}}$$

$$V_{\mathit{CTki}}^{\prime }=-\frac{u_i^2}{G\cdot \mathrm{L.}}\cdot \frac{f_x\cdot Z_{\mathit{\delta s}}^{\prime }\cdot \left({\delta }_{\mathit{ski}}-{\delta }_{\mathit{sn}}\right)+Z_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bki}}-{\delta }_{\mathit{bn}}\right)}{\cos \left({\varphi }_{\mathit{ki}}\right)}$$

$$V_{\mathit{TTki}}^{\prime }=\frac{1}{\mathrm{\Delta }{x}_{\mathit{TT}}^{\prime }}\left(\frac{u_i^2}{G\cdot \mathrm{L.}}\cdot \frac{f_x\cdot {\mathrm{M.}}_{\mathit{\delta s}}^{\prime }\cdot \left({\delta }_{\mathit{ski}}-{\delta }_{\mathit{sn}}\right)+{\mathrm{M.}}_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bki}}-{\delta }_{\mathit{bn}}\right)}{\cos \left({\varphi }_{\mathit{ki}}\right)}-x_{\mathit{CT}}^{\prime }\cdot V_{\mathit{CTki}}^{\prime }\right)$$

The fill volumes of the control cell V _{CT 1} and V _{CT 2} and the trim cell fillings V _{TT 1} and V _{TT 2} for trim and weight states of the submarine, identified by the index k = 1 and k = 2, result as mean values of the V _{CT 1 i '} V _{CT 2 i} , V _{TT 1 i} and V _{TT 2 i} values.

$Z_{\mathit{\delta s}}^{\prime },$

$Z_{\mathit{\delta b}}^{\prime },$

$M_{\ast }^{\prime }$

, $M_{\mathit{\delta s}}^{\prime }$

und $M_{\mathit{\delta b}}^{\prime },$

die Füllvolumen der Regelzelle V _CT1 und V _CT2 , die Trimmzellenfüllungen V _TT1 und V_TT2 und die Ruderwinkel δ_sn und δ_bn für auftrieb- und momentfreie Fahrt bestimmt.In particular, by evaluating the test series a) the coefficients $Z_{\ast }^{\prime },$

$Z_{\mathit{\delta s}}^{\prime },$

$Z_{\mathit{\delta b}}^{\prime },$

${\mathrm{M.}}_{\ast }^{\prime }$

, ${\mathrm{M.}}_{\mathit{\delta s}}^{\prime }$

and ${\mathrm{M.}}_{\mathit{\delta b}}^{\prime },$

the filling volume of the control cell V _{CT 1} and V _{CT 2} , the trim cell fillings V _{TT 1} and V _TT2 and the rudder angles δ _sn and δ _{bn are determined} for lift and torque-free travel.

Subsequently, the measured values determined in steps e) to l) are evaluated for trips with an aft or preloaded statically trimmed boat.

The following applies here:

$$\left(\begin{array}{ccc}{Z}_{\mathrm{W.}}^{\prime }& Z_{\mathrm{W.}\left|\mathrm{W.}\right|}^{\prime }& Z_{\mathit{\delta s\eta }}^{\prime }\end{array}\right)\left(\begin{array}{c}\tan \left({\theta }_i\right)\\ \tan \left({\theta }_i\right)\left|\tan \left({\theta }_i\right)\right|\\ f_x\cdot \left({\eta }_i\cdot \mathrm{C.}-1\right)\cdot {\delta }_{\mathit{si}}\end{array}\right)=-\frac{G\cdot \mathrm{L.}\cdot V_{\mathit{CTi}}^{\prime }}{u_i^2}\cdot \cos \left({\theta }_i\right)\cdot \cos \left({\varphi }_i\right)-Z_{\mathit{\delta s}}^{\prime }\cdot f_x\cdot \left({\delta }_{\mathit{si}}-{\delta }_{\mathit{sn}}\right)-Z_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bi}}-{\delta }_{\mathit{bn}}\right)$$

$$\left(\begin{array}{cccc}{\mathrm{M.}}_{\mathrm{W.}}^{\prime }& {\mathrm{M.}}_{\mathrm{W.}\left|\mathrm{W.}\right|}^{\prime }& {\mathrm{M.}}_{\mathit{\delta s\eta }}^{\prime }& z_{\mathit{GB}}^{\prime }\end{array}\right)\left(\begin{array}{c}\tan \left({\theta }_i\right)\\ \tan \left({\theta }_i\right)\left|\tan \left({\theta }_i\right)\right|\\ f_x\cdot \left({\eta }_i\cdot \mathrm{C.}-1\right)\cdot {\delta }_{\mathit{si}}\\ -\frac{G\cdot \mathrm{L.}\cdot V\prime }{u_i^2}\cdot \sin \left({\theta }_i\right)\end{array}\right)=-\frac{G\cdot \mathrm{L.}}{u_i^2}\cdot \left[\left(x_{\mathit{CT}}^{\prime }\cdot V_{\mathit{CTi}}^{\prime }+x_{\mathit{TT}}^{\prime }\cdot V_{\mathit{TTi}}^{\prime }\right)\cdot \cos \left({\theta }_i\right)\cdot \cos \left({\varphi }_i\right)+z_{\mathit{CT}}^{\prime }\cdot V_{\mathit{CTi}}^{\prime }\cdot \sin \left({\theta }_i\right)\right]-{\mathrm{M.}}_{\mathit{\delta s}}^{\prime }\cdot f_x\cdot \left({\delta }_{\mathit{si}}-{\delta }_{\mathit{sn}}\right)-{\mathrm{M.}}_{\mathit{\delta b}}^{\prime }\cdot \left({\delta }_{\mathit{bi}}-{\delta }_{\mathit{bn}}\right)$$

Where is:

  ein dimensionsloser Wert,
z_Gn   die z-Komponente des Gewichtsschwerpunkts des Bootes einschließlich gefluteter Freiräume für den Zustand der auftriebs- und momentfreien Fahrt,
z_B   die z-Koordinate des Auftriebsschwerpunkts der Formverdrängung im bootsfesten Koordinatensystem.
z _GB the stability _{lever arm} z _GB = z Gn - z _B ,
$z_{\mathit{GB}}^{\prime }=\frac{z_{\mathit{GB}}}{\mathrm{L.}}$

a dimensionless value,
z _Gn the z-component of the center of gravity of the boat including flooded clearances for the state of buoyancy and torque-free travel,
z _B the z -coordinate of the lift center of gravity of the shape displacement in the boat-fixed coordinate system.

The determination is made from the measured data by means of multilinear regression using the variables already known from a).

$Z_{w\left|w\right|}^{\prime },$

$Z_{\mathit{\delta s\eta }}^{\prime },$

$M_w^{\prime },$

$M_{w\left|w\right|}^{\prime },$

und $M_{\mathit{\delta s\eta }}^{\prime }$

und der Stabilitätshebelarm z_GB bestimmt.In particular, the coefficients $Z_w^{\prime },$

$Z_{w\left|w\right|}^{\prime },$

$Z_{\mathit{\delta s\eta }}^{\prime },$

${\mathrm{M.}}_w^{\prime },$

${\mathrm{M.}}_{w\left|w\right|}^{\prime },$

and ${\mathrm{M.}}_{\mathit{\delta s\eta }}^{\prime }$

and the stability lever arm z _GB determined.

• n) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei einer dritten ersten Geschwindigkeit und einer ersten ersten Trimmlage,
• o) beschleunigungsfreie Fahrt mit ebenem Kiel bei konstanter Tiefe und bei einer dritten ersten Geschwindigkeit und einer zweiten ersten Trimmlage.

In a further embodiment of the invention, the following steps are carried out in addition to steps a) to d):

• n) acceleration-free travel with a level keel at constant depth and at a third first speed and a first first trim position,
• o) Acceleration-free travel with a level keel at constant depth and at a third first speed and a second first trim position.

Further first speeds, in particular a total of five to eight first speeds, particularly preferably six first speeds, are particularly preferably used.

• p) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer dritten zweiten Geschwindigkeit und einer ersten vorderen Tiefenruderlage und einer ersten Trimmtankfüllung,
• q) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer dritten zweiten Geschwindigkeit und einer zweiten vorderen Tiefenruderlage und einer ersten Trimmtankfüllung,
• r) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer dritten zweiten Geschwindigkeit und einer ersten vorderen Tiefenruderlage und einer zweiten Trimmtankfüllung,
• s) beschleunigungsfreie Fahrt mit schrägem Kiel bei konstanter Tiefe und bei einer dritten zweiten Geschwindigkeit und einer zweiten vorderen Tiefenruderlage und einer zweiten Trimmtankfüllung.

In a further embodiment of the invention, the following steps are carried out in addition to steps e) to h):

• p) acceleration-free travel with an inclined keel at constant depth and at a third second speed and a first forward depth rudder position and a first trim tank filling,
• q) Acceleration-free travel with an inclined keel at constant depth and at a third second speed and a second forward depth rudder position and a first trim tank filling,
• r) Acceleration-free travel with an inclined keel at constant depth and at a third second speed and a first forward depth rudder position and a second trim tank filling,
• s) Acceleration-free travel with a sloping keel at constant depth and at a third, second speed and a second forward depth rudder position and a second trim tank filling.

Further second speeds, in particular a total of four to eight second speeds, particularly preferably five second speeds, are particularly preferably used.

In a further embodiment of the invention, the first speeds are selected from the range from 4 kn to 25 kn, preferably from the range from 5 kn to 20 kn, particularly preferably from the range from 6 kn to 15 kn.

In a further embodiment of the invention, the second speeds are selected from the range from 4 kn to 25 kn, preferably from the range from 5 kn to 20 kn, particularly preferably from the range from 6 kn to 14 kn.

In a further embodiment of the invention, an angle of + 15 ° to + 25 °, in particular + 18 ° to + 22 °, is selected as the first forward elevator position and an angle of -15 ° to -25 ° is selected as the second forward elevator position, selected in particular from -18 ° to -22 °.

In a further embodiment of the invention, the method is carried out in such a way that the diving depth is selected so that at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, water above the submarine and at least 25 m, preferably at least 50 m , particularly preferably at least the length of the submarine, are water under the submarine.

This procedure determines the hydrodynamic coefficients in the unaffected deep water area.

In a further embodiment of the invention, the method is carried out in such a way that the diving depth is chosen so that less than 25 m, preferably less than 15 m, water above the submarine and at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, there are water under the submarine.

This procedure determines the hydrodynamic coefficients in the near-surface area and is important for snorkeling, for example. This method is preferably used in addition to the determination in the unaffected deep water area.

In a further embodiment of the invention, the method is carried out in such a way that the diving depth is selected so that at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, water above the submarine and less than 25 m, preferably less than 15 m, there are water under the submarine.

This procedure determines the hydrodynamic coefficients in the area close to the ground and is important, for example, for submerged trips in shallow water. This method is preferably used in addition to the determination in the unaffected deep water area.

According to the invention, the speed u of the submarine, the front depth rudder angle δ _s , the rear depth rudder angle δ _b , the change in volume of the trim tanks Δ V _TT and the change in volume of the control cell Δ V _CT are recorded during the acceleration-free journeys.

In a further embodiment of the invention, the speed of rotation n of the screw and the trim angle θ are additionally recorded during the acceleration-free journeys.

In a further embodiment of the invention, the roll angle φ and the change in volume of the ballast tank Δ V _CT are also recorded during the acceleration-free journeys.

In a further embodiment of the invention, the weight distribution in the submarine is kept constant except for the targeted changes during the method. In particular, care is taken that the crew does not change their position, as this leads to non-detectable mass displacements and thus reduces the measurement accuracy of the method.

$Z_{\mathit{\delta b}}^{\prime },$

$M_{\ast }^{\prime },$

$M_{\mathit{\delta s}}^{\prime }$

und $M_{\mathit{\delta b}}^{\prime },$

die Füllvolumen der Regelzelle V _CT1 und V _CT2 die Trimmzellenfüllungen V _TT1 und V_TT2 und die Ruderwinkel δ_sn und δ_bn für auftrieb- und momentfreie Fahrt bestimmt.In a further embodiment of the invention, the coefficients $Z_{\ast }^{\prime },Z_{\mathit{\delta s}}^{\prime },$

$Z_{\mathit{\delta b}}^{\prime },$

${\mathrm{M.}}_{\ast }^{\prime },$

${\mathrm{M.}}_{\mathit{\delta s}}^{\prime }$

and ${\mathrm{M.}}_{\mathit{\delta b}}^{\prime },$

the fill volume of the control cell V _{CT 1} and V _{CT 2,} the trim cell fillings V _{TT 1} and V _TT2 and the rudder angles δ _sn and δ _bn for buoyancy and torque-free travel.

In a further embodiment of the invention, the first first trim position and the second first trim position are selected to be different by 500 kNm ± 50 kNm.

In a further embodiment of the invention, a first, second trim position and a second, second trim position are selected in steps e) and l), the first, second trim position and the second, second trim position being selected to be different by 1000 kNm ± 100 kNm.

$Z_{w\left|w\right|}^{\prime },$

$Z_{\mathit{\delta s\eta }}^{\prime },$

$M_w^{\prime },$

$M_{w\left|w\right|}^{\prime },$

und $M_{\mathit{\delta s\eta }}^{\prime }$

und der Stabilitätshebelarm z_GB bestimmt.In a further embodiment of the invention, the coefficients are in step m) $Z_w^{\prime },$

$Z_{w\left|w\right|}^{\prime },$

$Z_{\mathit{\delta s\eta }}^{\prime },$

${\mathrm{M.}}_w^{\prime },$

${\mathrm{M.}}_{w\left|w\right|}^{\prime },$

and ${\mathrm{M.}}_{\mathit{\delta s\eta }}^{\prime }$

and the stability lever arm z _GB determined.

Fig. 1

Darstellung der Vektoren und Winkel am Unterseeboot

When the submarine is traveling without acceleration, static forces applied by changing the tank fillings are compensated for by flow forces on the rudder and hull. Since the flow forces increase with the square of the driving speed in submerged travel, while the static forces remain constant, there is the possibility of determining the flow forces or hydrodynamic coefficients from the compensation of known statically introduced weight forces with previously unattained accuracy. All measurement trips are carried out at different constant speeds and different predetermined trim angles of the boat by placing the front and rear depth rudders accordingly at a constant depth. This makes it possible to determine hydrodynamic coefficients as a function of the depth of the boat or the distance between the boat and the surface of the water.

Fig. 1

Representation of the vectors and angles on the submarine

In Fig. 1 the angles and sizes are shown using the example of a submarine with a cross rudder.

Claims (15)

1. Method for determining hydrodynamic coefficients in submarines comprising a front hydroplane and a rear hydroplane, wherein the submarine is free-floating, wherein the method comprises the following steps:

   a) acceleration-free travel with an even keel at a constant depth and at a first first speed and a first first trim position,

   b) acceleration-free travel with an even keel at a constant depth and at the first first speed and a second first trim position,

   c) acceleration-free travel with an even keel at a constant depth and at a second first speed and the first first trim position,

   d) acceleration-free travel with an even keel at a constant depth and at the second first speed and the second first trim position,

   e) acceleration-free travel with an uneven keel at a constant depth and at a first second speed and a first front hydroplane position and a first trim tank filling,

   f) acceleration-free travel with an uneven keel at a constant depth and at the first second speed and a second front hydroplane position and the first trim tank filling,

   g) acceleration-free travel with an uneven keel at a constant depth and at the first second speed and the first front hydroplane position and a second trim tank filling,

   h) acceleration-free travel with an uneven keel at a constant depth and at the first second speed and the second front hydroplane position and the second trim tank filling,

   i) acceleration-free travel with an uneven keel at a constant depth and at a second second speed and the first front hydroplane position and the first trim tank filling,

   j) acceleration-free travel with an uneven keel at a constant depth and at the second second speed and the second front hydroplane position and the first trim tank filling,

   k) acceleration-free travel with an uneven keel at a constant depth and at the second second speed and the first front hydroplane position and the second trim tank filling,

   l) acceleration-free travel with an uneven keel at a constant depth and at the second second speed and the second front hydroplane position and the second trim tank filling,

   m) determination of hydrodynamic coefficients from the measuring variables determined in the preceding steps,

   wherein steps a) to 1) are carried out in any sequence, wherein step m) is carried out after steps a) to 1), wherein, during the acceleration-free travels, in each case the speed u of the submarine, the trim angle θ, the front hydroplane position δ_s , the rear hydroplane angle δ_b , the change in volume of the trim tanks ΔV_TT and the change in volume of the depth control tank ΔV_CT are detected as measuring variables.
2. Method according to Claim 1, characterized in that, in addition to steps a) to d), the following steps are carried out:

   n) acceleration-free travel with an even keel at a constant depth and at a third first speed and a first first trim position,

   o) acceleration-free travel with an even keel at a constant depth and at a third first speed and a second first trim position.
3. Method according to either of the preceding claims, characterized in that, in addition to steps e) to 1), the following steps are carried out:

   p) acceleration-free travel with an uneven keel at a constant depth and at a third second speed and a first front hydroplane position and a first trim tank filling,

   q) acceleration-free travel with an uneven keel at a constant depth and at a third second speed and a second front hydroplane position and a first trim tank filling,

   r) acceleration-free travel with an uneven keel at a constant depth and at a third second speed and a first front hydroplane position and a second trim tank filling,

   s) acceleration-free travel with an uneven keel at a constant depth and at a third second speed and a second front hydroplane position and a second trim tank filling.
4. Method according to one of the preceding claims, characterized in that the first speeds are selected from the range of 4 kn to 25 kn, preferably from the range of 5 kn to 20 kn, particularly preferably from the range of 6 kn to 15 kn.
5. Method according to one of the preceding claims, characterized in that the second speeds are selected from the range of 4 kn to 25 kn, preferably from the range of 5 kn to 20 kn, particularly preferably from the range of 6 kn to 14 kn.
6. Method according to one of the preceding claims, characterized in that an angle of + 15° to + 25°, in particular of + 18° to + 22°, is chosen as the first front hydroplane position and in that an angle of - 15° to - 25°, in particular of - 18° to - 22°, is chosen as the second front hydroplane position.
7. Method according to one of the preceding claims, characterized in that the method is carried out in such a way that the diving depth is chosen such that there is at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, of water above the submarine and at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, of water under the submarine.
8. Method according to one of Claims 1 to 6, characterized in that the method is carried out in such a way that the diving depth is chosen such that there is less than 25 m, preferably less than 15 m, of water above the submarine and at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, of water below the submarine.
9. Method according to one of Claims 1 to 6, characterized in that the method is carried out in such a way that the diving depth is chosen such that there is at least 25 m, preferably at least 50 m, particularly preferably at least the length of the submarine, of water above the submarine and less than 25 m, preferably less than 15 m, of water below the submarine.
10. Method according to one of the preceding claims, characterized in that the rotational speed n of the propeller and the rolling angle φ are additionally detected as measuring variables.
11. Method according to one of the preceding claims, characterized in that, while moving, the weight distribution in the submarine is kept constant apart from the targeted changes.
12. Method according to one of the preceding claims, characterized in that, in step m), the coefficients Z'_*, Z'_δs, Z'_δb, M'_*, M'_δs, M'_δb, the filling volumes of the depth control tank V_CT1 and V_CT2, the trim tank fillings V_TT1 and V _TT2 and the hydroplane angles δ_sn and δ_bn are determined for buoyancy-free and moment-free travel.
13. Method according to one of the preceding claims, characterized in that the first first trim position and the second first trim position are chosen to be different by 500 kNm ± 50 kNm.
14. Method according to one of the preceding claims, characterized in that, in steps e) to 1), a first second trim position and a second second trim position are chosen, wherein the first second trim position and the second second trim position are chosen to be different by 1000 kNm ± 100 kNm.
15. Method according to one of the preceding claims, characterized in that, in step m), the coefficients Z'_w, Z'_w / _w /, Z'_δsη, M'_w, M' _w/w/ , M'_δsη and the stability lever arm z_GB are determined.

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