JP6298940B1 - Flying object injection energy measuring device and flight characteristic acquisition program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a measuring device for accurately predicting the flight distance of a flying object by a simple method and a program for acquiring the flight distance based on the output thereof. A measuring apparatus includes a rotating body that is rotatably supported by a rotating shaft of a main body. A plastic bottle rocket (flying body) 1 is attached to the other end of the rotator 120, and the rotator 120 rotates according to the injection energy when the plastic bottle rocket 1 is launched. The detection unit 150 detects the maximum rotation angle θmax of the rotating body. The computer 200 calculates the maximum rotation angle θcal based on various parameters related to the injection of the plastic bottle rocket 1. The computer 200 calculates the polytropic index n of the plastic bottle rocket 1 based on the detected value θmax and the calculated value θcal. The polytropic index n is used for obtaining the flight distance of the plastic bottle rocket 1. [Selection] Figure 3

Description

  The present invention relates to an injection energy measuring apparatus and flight characteristic acquisition program for a flying object using a high-pressure liquid or gas injected therein as a power source, and more particularly to an injection energy measuring apparatus and a flight characteristic acquisition program for a PET bottle rocket.

As an educational activity of schools, experimental learning of rockets using plastic bottles (plastic bottle rockets) is being conducted in order to learn the principles of rockets as flying objects.
Such PET bottle rocket learning is conducted nationwide, and competitions are held to compete for the flight distance and the accuracy of the landing point (flight direction).

In learning with a plastic bottle rocket, in order to determine the flight distance and flight direction,
(1) “Pressure” in a plastic bottle rocket
(2) “Water volume” and “Air volume” in the PET bottle rocket before launch
(3) the cross-sectional area of the nozzle,
(4) Various parameters such as “skirt shape” provided on the outer periphery of the main body of the PET bottle rocket are appropriately determined, and how the PET bottle rocket actually fired by these will fly, its flight distance, Learning such as measuring the direction of flight is conducted.

At the actual learning site, students compare the various parameters of the PET bottle rocket determined before the experiment with the actual flight distance and flight direction obtained when the PET bottle rocket was launched. Various parameters of the PET bottle rocket were decided when doing.
However, in the method of reflecting the above experimental results in the next production of the plastic bottle rocket, in order to obtain the plastic bottle rocket having the desired “flight characteristics (for example, flight distance)”, the production of the plastic bottle rocket, It was necessary to repeat the process of launch experiment (measurement of flight distance / direction of flight), determination of PET bottle rocket parameters based on the experiment results, and the next launch experiment.

Here, regarding the flight direction, the shape of the skirt attached to the outer periphery of the PET bottle rocket may be determined, and the adjustment of the flight direction is relatively easy. On the other hand, it has been difficult to accurately predict the flight distance to be a desired distance.
Therefore, the inventor of the present application determines the flight distance of the PET bottle rocket by “air resistance” of the PET bottle rocket, “flow coefficient (corresponding to the effective opening area of the injection nozzle)” of the fluid from the injection nozzle of the PET bottle rocket, etc. We examined whether it could be predicted.
As a result of this study, if the “polytropic index” determined by the relationship between pressure and volume can be known for PET bottle rockets, the flight distance can be accurately predicted based on the above “air resistance” and “flow coefficient”. It came to the idea that it should be.

However, a method for accurately obtaining a polytropic index (hereinafter referred to as “n”) unique to each plastic bottle rocket was not found, and accurate prediction could not be achieved.
Here, the polytropic index “n” itself is an index that is also used when measuring the internal volume and internal pressure of an engine cylinder in an internal combustion engine such as an automobile engine. In this technical field, the polytropic index “n” is used. There are a number of prior art techniques for acquiring the following.

Japanese Patent Laying-Open No. 2015-169149 (Japanese Patent Application No. 2014-259795) In this patent publication, the polytropic index “n” is obtained from the relationship between “pressure” and “volume” in the adiabatic change, and the acquisition method according to this patent publication is applied to the plastic bottle rocket according to the present application. When applied, the following problems arise.
In other words, in a plastic bottle rocket, air and water are sealed in a high pressure state inside, and a propulsive force (injection energy) can be obtained by ejecting the high pressure water and air at the time of launch. The flight characteristics can be obtained using the ideal gas equation.
However, when the ideal gas equation is used to predict the flight characteristics (flight distance) of a PET bottle rocket, it is necessary to analyze the relationship among the pressure (P), gas volume (V), and internal temperature in the PET bottle rocket. However, since these values change in a complicated manner with time, it is not practical to directly measure these values using an experimental apparatus.

Here, it is known that the relationship between the pressure (P) and the volume (V) is expressed by the following equation (1) in the state change of gas pressure / gas volume in the adiabatic change.
^PVγ = constant (1)
In formula (1), γ is a specific heat ratio. It is also known that the relationship between gas pressure (P) and gas volume (V) is expressed by the following formula (2) in the state change of isothermal change. .
PV = constant (2)

Here, based on the relationship between the pressure (P) and volume (V) of these gases, the relationship between the pressure and volume of the gas in the rocket in the PET bottle rocket experiment will be considered.
In the case of a plastic bottle rocket, the relationship between pressure (P) and volume (V) is neither the above-mentioned adiabatic change (formula (1)) nor the above-mentioned isothermal change (formula (2)), so-called “quasi-adiabatic change”. Therefore, in order to approximate this, it is desirable to obtain the polytropic index “n”.
That is, the relationship between the internal pressure (P) and the volume (V) in the PET bottle rocket is the following equation (3) using the polytropic index “n” used in thermodynamics (polytropic change).
PV ⁿ = constant (3)
The polytropic index “n” satisfies the following expression (4).
1 <n <γ (4)
Here, γ is a specific heat ratio of constant pressure molar specific heat and constant volume molar specific heat.
The polytropic index “n” is an index “n” when the following equation (5) is established between the absolute temperature T and the gas volume V.
T = K × V ^(1-n) (5)
Where K is a proportional constant

When predicting the flight characteristics (flight distance) of the actually launched PET bottle rocket, if the above-mentioned polytropic index “n” can be obtained in advance, the pressure applied to the inside of the PET bottle rocket, the effective opening area of the injection nozzle, By determining, the injection energy can be adjusted, so that desired flight characteristics (flight distance) according to the purpose can be obtained.
Thus, as described above, a method for obtaining the polytropic index “n” in a change state that is neither an adiabatic change nor an isothermal change, such as a PET bottle rocket, could not be realized because there is no known technical literature.

  The present invention has been made in view of such circumstances, and a measuring device capable of measuring the injection energy of a flying object that is launched with the energy obtained by the injection of the liquid or gas sealed inside, at a high pressure. And a procedure for obtaining a polytropic index based on a value measured by the measuring device and predicting a flight characteristic of the flying object, particularly a flight distance, based on the obtained polytropic index. For the purpose.

In order to solve the above-mentioned problems, a first invention of the present application is an apparatus for measuring an injection energy of a flying object that flies by injection energy, the apparatus including a main body provided with a rotation shaft and one end of the rotation shaft. A rotating body that is rotatably supported by the other end and provided with an attachment portion to which the flying object is attached to the other end, and detects the maximum rotation angle of the rotating body that rotates according to the jet energy when the flying object is launched. And a detection unit to be provided.
According to a second aspect of the present invention, the detection unit outputs the detected maximum rotation angle of the rotating body as an electrical signal.
According to a third aspect of the present invention, the flying object to be attached has an injection nozzle, and a gas and a liquid pressurized to a predetermined pressure are sealed inside the flying object. When the opening is made, the gas or liquid is jetted to the outside of the flying object to obtain a propulsive force.

According to a fourth aspect of the present invention, the flying object is a plastic bottle rocket, water is used as the liquid, and air is used as the gas.
Further, a fifth invention of the present application is a program for acquiring a flight distance of a flying object, the step of recognizing the maximum dog rotation angle of the rotating object based on a signal from the detection unit described above, Calculating the maximum rotation angle of the rotating body based on the outflow state of the liquid and gas inside the flying body, the rotating state of the rotating body, and the change state of the liquid and gas inside the flying body, and the recognized maximum The method includes a step of obtaining a polytropic index of the flying object based on a rotation angle and the calculated maximum rotation angle, and a step of acquiring a predicted value of a flying distance of the flying object based on the polytropic index.

  Further, a sixth invention of the present application is a program for acquiring the flying distance of a flying object, the step of recognizing the maximum rotation angle of the rotating body based on a signal from the detection unit described above, and the flying object Recognizing the air resistance of the flying object, recognizing the effective opening area of the jet nozzle of the flying object, at least the mass of the liquid enclosed in the flying object, the pressure applied to the inside, and the launch of the flying object Recognizing the angle, and calculating the maximum rotation angle of the rotating body based on the outflow state of the liquid and gas inside the flying body, the rotating state of the rotating body, and the change state of the liquid and gas inside the flying body A step of determining a polytropic index of the flying object based on the recognized maximum rotation angle and the calculated maximum rotation angle, the polytropic index, and the recognized air resistance. When, is made of a step of calculating the flight distance of the projectile on the basis of the effective opening area of the injection nozzle described above recognition.

According to the first invention of the present application, the jet energy of the flying object can be detected by a simple measuring device.
Further, according to the second invention of the present application, based on a signal from the measuring device indicating the maximum rotation angle of the rotating body that changes according to the jetting energy of the flying object, the computer or the like can determine the flight characteristics of the flying object (for example, Flight distance) can be predicted.
Further, according to the third invention of the present application, it is possible to detect the injection energy for easily predicting the flight characteristics of the flying object having the injection nozzle.
Further, according to the fourth invention of the present application, it is possible to detect the injection energy for easily and accurately predicting the flight characteristics of the PET bottle rocket used at the learning site.
Further, according to the fifth or sixth invention of the present application, the flight characteristics (for example, flight distance) of the flying object can be predicted easily and accurately by a computer.

Embodiments of the present invention will be described below.
First, a measuring apparatus 100 according to the present invention will be described with reference to FIGS.
The measuring device 100 is a device that measures a physical quantity (maximum rotation angle θmax of the rotating bar 120) indicating the injection energy of a plastic bottle rocket (flying object) 1 into which water (liquid) is injected. , The rotating bar (rotating body) 120 is configured to rotate to a rotation angle (maximum rotation angle θmax) corresponding to the magnitude of the injection energy, and this maximum rotation angle θmax is used as the emission energy of the PET bottle rocket 1. It can be easily measured as a parameter indicating.

Specifically, as shown in FIG. 1, the measuring device 100 includes a main body 110, a rotating bar (rotating body) 120, a mounting portion 130, an adjusting portion 140, and a rotation angle detecting device 150.
The main body 110 includes a rotary bar support 110A, a rotary bar receiver 110B, and a bottom plate 110C to which these are fixed. 110 C of bottom plate parts are fixed to the ground etc. at the time of an injection experiment, and even if the plastic bottle rocket 1 is injected, 110 A of rotation bar support parts do not move.
One end 121 of the rotating bar 120 is rotatably attached to the rotating shaft 111 of the rotating bar support 110A, and the other end 122 is provided with an attaching part 130 for attaching the plastic bottle rocket 1. Further, the rotating bar 120 is held in a ready state by the rotating bar receiving portion 110B before and after the injection of the plastic bottle rocket 1.

As shown in FIG. 2, the mounting portion 130 has a support plate 131 fixed to the other end 122 of the rotating bar 120 with a bolt / nut, and a “necked portion” between the PET bottle rocket 1 body and the injection nozzle 1A. The fixing plate 132 is sandwiched and fixed.
The fixing plate 132 is fixed to the support plate 131 with bolts and nuts in a state where the “necked portion” of the plastic bottle rocket 1 is sandwiched.
Thereby, even when the plastic bottle rocket 1 is ejected at the time of the injection experiment, the plastic bottle rocket 1 is not separated from the rotating bar 110.

Returning to the description of FIG. 1, the rotating bar 120 is provided with an adjusting unit 140 for adjusting the rotating moment. The adjustment unit 140 includes a weight 141 and a rail 142 (indicated by a broken line in the drawing) provided on the rotating bar 120. The weight 141 moves on the rail 142 in the axial direction of the rotating bar 120 (horizontal in FIG. 1). Direction).
A fixing member (not shown) is provided between the weight 141 and the rail 142 so that the weight 141 can be fixed at an arbitrary position (Lw position in the illustrated example) on the rail 142.
For example, using the measuring apparatus 100 having a distance (Lr) from the rotation shaft 111 to the center of the mounting portion 130 of the PET bottle rocket 1 of 935 mm and a weight 141 of 3.51 kg, the PET bottle rocket 1 having a capacity of 1.5 L If an injection experiment is performed, when the amount of water to be filled in the PET bottle rocket 1 is 0.5 L and the pressure of the water after pressurization is 3 atm, the slide position of the weight 141 is 275 mm (Lw from the rotation shaft 111). ).
Note that the measuring apparatus 100 is designed to measure the maximum rotation angle θmax according to the injection energy even when the water pressure in the PET bottle rocket 1 is increased to 3 to 7 atmospheres (gauge pressure). ing.

Prior to the PET bottle rocket 1 injection experiment, the position of the weight 141 is adjusted to an arbitrary distance (Lr) from the rotating shaft 111 so that even if the instantaneous propulsive force of the PET bottle rocket 1 is maximized, the rotation is possible. The maximum rotation angle θmax at the time of injection of the bar 110 can be adjusted to a desired range (for example, 70 degrees <θ <90 degrees) (FIG. 3).
In this way, by adjusting the mass of the weight 141 and the slide position of the adjusting unit 140 and adjusting the maximum rotation angle θmax of the rotating bar 120 between 70 degrees and 90 degrees during the injection experiment, the rotating bar 120 actually rotates. The angle to be measured can be increased, the influence of measurement errors can be minimized, and the measurement accuracy of the maximum rotation angle θmax can be increased.
In preparation for the case where the injection energy of the PET bottle rocket 1 becomes an unexpected value, a stopper 113 (safety device) is provided on the rotating bar support 110A so that the rotating bar 120 cannot rotate more than 90 degrees.

The rotation angle detection device 150 is for detecting the actual maximum rotation angle θmax of the rotating bar 120 when the PET bottle rocket 1 is jetted, and rotates while water and air inside the PET bottle rocket 1 are being jetted. A value indicating the maximum rotation angle (θmax) of the bar 120 is converted into an electric signal and sent to the computer 200 via a cable (signal line) 160 (FIG. 4).
In FIG. 1, reference numeral 10 is a pump for pressurizing the inside of the plastic bottle rocket 1, and reference numeral 20 is a pressure gauge for accurately adjusting the pressure (gauge pressure) in the plastic bottle rocket 1. is there. Reference numeral 30 denotes a pressurizing valve attached to the injection nozzle 1A of the plastic bottle rocket 1 during pressurization.

As shown in FIG. 3, the measuring apparatus 100 configured as described above is configured such that when the PET bottle rocket 1 is injected, the rotating bar 120 is rotated clockwise in the drawing around the rotating shaft 111 by the injection energy. (Rotation angle θmax).
The rotation angle θmax at this time is detected by the rotation angle detector 150 as described above, and a signal representing the detection result (θmax) is output to the computer 200.

Next, a procedure for predicting the flight distance (flight characteristics) of the plastic bottle rocket (flying object) 1 based on the measurement result of the maximum rotation angle (θmax) sent from the rotation angle detection device 150 of the measurement device 100. Will be described. In this embodiment, the flight distance is predicted by the computer 200.
FIG. 5 is a flowchart showing an outline of a flight distance prediction program executed by the computer 200.
When this flight distance prediction program is started, in step 1, the maximum rotation angle θmax (actual value) obtained by the injection experiment obtained by the measurement apparatus 100 is recognized based on the signal from the rotation angle detection device 150.
In step S2, a theoretical value (calculated value θcal) of the maximum rotation angle is calculated based on various parameters, and the polytropic index “n” is calculated based on the calculated value θcal and the actual measured value θmax of the maximum rotation angle recognized in step S1. Is determined.
In the next step S3, a flight distance (predicted value) that will be reached when the plastic bottle rocket 1 is actually fired is obtained using this polytrol index “n”.

Next, “rotation angle (θcal) calculation processing / polytropic index“ n ”acquisition processing using the rotation angle (θcal)” performed in step S2 of the above-described flight distance prediction program (FIG. 5) will be described with reference to the program flowchart of FIG. .
When this program is started, first, initial values of various parameters input to the computer 200 in advance are read in step S201.
In this step S201, for example,
(1) Initial value of pressure P (gauge pressure) inside the PET bottle rocket 1 (2) Initial value of volume Vw of water injected into the PET bottle rocket 1 (3) Air volume Va inside the PET bottle rocket 1 The initial value of is set.
further,
(4) Determination of the effective opening area Se based on the opening area S of the injection nozzle 1A (5) The air density ρt inside the PET bottle rocket 1 is calculated.
The calculation of the air density ρ is performed by the following calculation formula (1).
ρt = ρ0 × (P0 + Pa) / Pa (1)
Here, Pa is atmospheric pressure, P0 is a set pressure (gauge pressure) applied to the inside of the plastic bottle rocket 1, and ρ0 is an air density at atmospheric pressure (Pa).

Returning to the description of FIG. 6, in step S202, the time t of the timer at this time is set to “0”, and the rotation angle θ is set to “0” (initial setting).
In step S203, when the pressurization valve 30 is removed from the injection nozzle 1A and the plastic bottle rocket 1 is launched, the “water outflow speed” when high-pressure water inside the plastic bottle rocket flows out of the plastic bottle rocket body. And each theoretical value of “outflow” per unit time is calculated. The calculation of the “water outflow rate” and the “water outflow amount” is performed by the program shown in FIG.

In step S204, theoretical values of “rotational torque” and “moment of inertia” generated in the rotating bar 120 while “water” is ejected from the plastic bottle rocket 1 are calculated. The calculation of “rotational torque” and “moment of inertia” is performed by the program shown in FIG.
In step S205, theoretical values of “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” when the rotating bar 120 rotates by the injection of “water” are calculated. The calculation of the “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” is performed by the program shown in FIG.
In step S206, the values of “water volume”, “air volume”, “air density”, “air temperature”, and “air pressure” in the PET bottle rocket 1 are updated. The values of “water volume”, “air volume”, “air density”, “air temperature”, and “air pressure” are updated by a program shown in FIG.

In step S207, the time “t” set in step S202 is updated.
In step S208, it is determined whether or not the actual measurement value of the water volume in the plastic bottle rocket 1 is “0” or more, that is, whether high-pressure “water” still remains in the plastic bottle rocket 1 or not.
If the determination result is “Yes”, that is, while high-pressure “water” remains in the PET bottle rocket 1, the process returns to step S203, and the processing from step S203 to step S207 described above is performed until there is no “water”. repeat.

When the determination result in step S208 turns to “No”, that is, when “water” in the plastic bottle rocket 1 disappears, and then high-pressure “air” is injected from the inside of the plastic bottle rocket 1, the process proceeds to step S211. The theoretical values of the “outflow velocity” of the “air” and the “outflow amount of air” per unit time are calculated. The calculation of the “air outflow speed” and the “air outflow amount” is performed by the program shown in FIG.
In step S212, theoretical values of “rotational torque” and “moment of inertia” generated in the rotary bar 120 while “air” is ejected from the plastic bottle rocket 1 are calculated. The calculation of “rotational torque” and “moment of inertia” is performed by the program shown in FIG.

In step S213, theoretical values of “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” when the rotating bar 120 rotates by air injection are calculated. The calculation of “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” is performed by the program shown in FIG.
In step S214, the values of “air volume”, “air density”, “air temperature”, and “air pressure” in the plastic bottle rocket 1 are updated. The values of “air volume”, “air density”, “air temperature”, and “air pressure” are updated by the program shown in FIG.

In step S215, it is determined whether or not the air pressure in the plastic bottle rocket 1 is still larger than the atmospheric pressure, that is, whether or not high-pressure “air” is still being injected from the plastic bottle rocket 1. Is called.
When the determination result is “Yes”, the time “t” is updated in the next step S216, and then the process returns to the above-described step S211.

If the determination result in step S215 is “Yes”, that is, while high-pressure “air” remains in the plastic bottle rocket 1, the process returns to step S211 until the high-pressure “air” in the plastic bottle rocket 1 is exhausted ( The process from step S211 to step S216 is repeated until the atmospheric pressure matches or becomes smaller.
When the determination result in step S215 turns to “No”, first, the time “t” is updated in step S221.

In the processing after step S222, after both the high-pressure “water” and “air” disappear from the inside of the plastic bottle rocket 1, the rotation angle is calculated when the rotating bar 120 rotates by inertial force.
First, in step S222, theoretical values of “rotational torque” and “moment of inertia” generated in the rotating bar 120 by inertial force are calculated. The calculation of “rotational torque” and “moment of inertia” is performed in the same procedure as in step S204 and step S212, and detailed description thereof is omitted.

In step S223, theoretical values of “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” when the rotating bar 120 rotates by inertial force are calculated. The calculation of “angular acceleration αθ”, “angular velocity ω”, and “rotation angle θ” is performed in the same procedure as in steps S205 and S213, and detailed description thereof is omitted.
In step S224, it is determined whether or not the angular velocity “ω” calculated in step S223 is greater than “0”, that is, whether or not the rotating bar 120 is still rotating due to inertial force.

When the determination result is “Yes”, the process returns to step S221, and the processes from step S221 to step S224 are repeated until the rotation of the rotation bar 120 stops.
If the determination result of step S224 turns to “No”, the process proceeds to step S225, and the rotation angle “θ” at this time is set as the calculated value (theoretical value) θcal of the maximum rotation angle.

In the next step S226, it is determined whether or not the calculated value θcal matches the actual measurement value θmax measured using the measuring apparatus 100.
While the determination result is “No”, the process proceeds to step S227, and it is determined whether or not the calculated value θcal is smaller than the actually measured value θmax.
While the calculated value θcal is smaller than the actually measured value θmax, the process proceeds to step S228, and the provisional value n of the polytropic index set at this time is increased by Δn (for example, 0.005), and from step S203 to step S226. Repeat the process up to.

  On the other hand, when the determination result in step S227 is “No”, that is, if the calculated value θcal is larger than the actual measurement value θmax, the process proceeds to step S229, and the provisional value n of the polytropic index set at this time point Is reduced by Δn (for example, 0.005), and the processing from step S203 to step S226 is repeated.

  When the determination result in step S226 turns to “Yes”, that is, when the calculated value θcal of the maximum rotation angle and the measured value θmax coincide, the value of the polytropic index set at this time is used as the PET bottle. Recognizing the actual polytropic index “n” of rocket 1, this program is terminated.

Next, various calculation processes performed in step S203, step S204, step S205, step S206, step S211, step S212, step S213, and step S214 described above will be described.
FIG. 7 is a flowchart showing a program for calculating “water outflow rate” and “water outflow amount” performed in step 203 of FIG.

First, in step S2031, the water outflow speed Uw at the time of injection of the plastic bottle rocket 1 is calculated using Graham's formula.
Uw = (2 × P / ρw) 1/2 (2)
Here, the pressure P is a gauge pressure applied to the plastic bottle rocket 1, and ρw is the density of water injected into the plastic bottle rocket 1.
In step S2032, the outflow amount ΔQw of water injected from the plastic bottle rocket 1 in Δt seconds is calculated, and in the next step S2033, the propulsive force Fw generated by the injection of water from the plastic bottle rocket 1 using Newton's second law. Is calculated by the following equation (3).
Fw = Se × Uw ² × ρw (3)
Here, Se is the “effective opening area” of the injection nozzle 1A.

FIG. 8 is a flowchart showing a program for calculating “rotational torque” and “moment of inertia” performed in step S204 of FIG.
By executing this program, the rotation angle of the rotating bar 120 when high-pressure “water” is being injected from the inside of the plastic bottle rocket 1 can be calculated.
The rotation angle of the rotary bar 120 due to the inertial force is a value corresponding to the weight of the weight 141 and the mass of “water” injected into the plastic bottle rocket 1.
Further, the moment applied to the rotating bar 120 around the rotating shaft 111 can be calculated based on the rotational torque and inertia torque due to gravity.

FIG. 9 is a flowchart showing the program executed in step S205 of FIG.
First, in step S2051, the angular acceleration αθ of the rotating bar 120 is calculated from the formula for the rotational motion of the rigid body.
Here, it is assumed that the difference between the torque applied to the rotating bar 120 and the torque Trq2 from the gravity due to the mass of the weight 141 is applied to the rotating bar 120 by the injection energy when water is injected from the plastic bottle rocket 1. .
In this case, the angular acceleration αθ of the rotating bar 120 is obtained by the following calculation formula (4).
αθ = (Fw × Lr−Trq2) / J2 (4)
Here, Fw is the propulsive force generated by the injection of the plastic bottle rocket 1, Lr is the distance between the rotating shaft 111 and the center of the mounting portion 130, and J2 is "moment of inertia".

In steps S2052 and S2053, the angular velocity ω of the rotation bar 120 and the rotation angle θ of the rotation bar 120 after Δt seconds have elapsed are calculated from the following equations (5) and (6), respectively.
ω = ω + αθ × Δt (5)
θ = θ + ω × Δt (6)
FIG. 10 is a flowchart showing a program for updating the values of “water volume”, “air volume”, “air density”, “air temperature”, and “air pressure” performed in step S206 of FIG.
The value of “water volume in the plastic bottle rocket” when Δt seconds elapses after reading of the initial value is calculated based on “amount of water released”, and this calculated value is set as an updated value.
Further, the value of “pressure in the PET bottle rocket” after Δt seconds can be calculated by using an equation of state change of polytropic change, and this value is set as an updated value.
For example, if the pre-update values of “air pressure” and “air volume” are (P1, V1) and the post-update values are (P2, V2), the post-update pressure based on the following relational expression (7) P2 can be obtained. The pressure used here is an absolute pressure, and “n” is a polytropic index.
P2 = P1 × (V1 / V2) ⁿ (7)

Here, if “n” is “1”, the relational expression is a constant temperature change, and it is considered that thermal energy is supplied from the outside during expansion, and the maximum work is performed on the outside.
On the other hand, if “n” is “γ (specific heat ratio)”, the relational expression in the adiabatic change is obtained, it is considered that there is no supply of heat energy from the outside, and the amount of work is the least for the outside.
When neither a constant temperature change nor an adiabatic change, the value of “n” satisfies the following equation (8).
1 <n <γ (8)
In this case, in order to know the relationship between the pressure P and the volume V, it is necessary to know the value of the polytropic index “n”.

In this embodiment, as described above, the polytropic index “n” is obtained by executing the program shown in FIG. 6 and the actually measured value (θmax) of the maximum rotation angle obtained by the measuring apparatus 100. It can be easily obtained using the calculated value (θcal) of the maximum rotation angle.
Since the polytropic index “n” can be easily obtained, the values of the pressure P and the volume V can be easily obtained (at real time) for each Δt as in the case of the internal combustion engine, and the polytropic index “n”. Can also be used for various controls.

FIG. 11 is a flowchart showing the program executed in step S211 of FIG.
First, in step S2111, the outflow speed Ua of air from the inside of the plastic bottle rocket 1 to the outside is calculated, and in the next step S2112 the outflow amount ΔQa of air is calculated. In step S2113, the injection energy Fa due to the ejection of air from the plastic bottle rocket 1 is calculated. The calculation method of the injection energy Fa is the same as the calculation of the injection energy of “water” described with reference to the flowchart of FIG. 7 described above, and the description thereof is omitted.

FIG. 12 is a flowchart showing the program executed in step S212 of FIG.
First, in step S2121, the moment of inertia J2 about the rotation axis 111 is calculated, and in the next step S2122, the rotational torque Trq2 due to gravity is calculated.

FIG. 13 is a flowchart showing the program executed in step S213 of FIG.
First, in step S2131, the angular acceleration αθ is calculated in the same procedure as in step S2051 in FIG.
When the weight 141 is not considered, the correction value when the weight 141 is provided for the moment of inertia J1 and the rotational torque Trq1 of the rotating bar 120 is considered.
Assuming that the difference between the rotational torque due to the ejection of “air” from the PET bottle rocket 1 at the time of launch and the rotational torque Trq2 due to gravity acts on the rotational bar 120, the angular acceleration αθ of the rotational bar 120 is expressed by the following equation (8). Is calculated by
αθ = (Fa × Lr−Trq2) / J2 (8)
Here, Fa is the injection energy (corresponding to the propulsive force) obtained by the injection of “air”, and Lr is the distance from the rotation shaft 111 to the center of the mounting portion 130 of the PET bottle rocket 1.
In the next step S2132, the angular velocity ω after Δt seconds is calculated by the following equation (9), and in step S2223, the angle θ is calculated by the following equation (10), respectively, and is set to the updated value.
ω = ω + αθ × Δt (9)
θ = θ + ω × Δt (10)
Δt is a constant value, and is 0.005 seconds in this embodiment.

FIG. 14 is a flowchart showing the program executed in step S214 of FIG.
This program is for updating the values of “air volume”, “air density”, “air temperature”, and “air pressure”.
The update of the various values described above by this program is performed in the same manner as the program of FIG. 10 already described, and therefore detailed description thereof is omitted. When this program is executed, no “water” remains in the plastic bottle rocket 1, so the maximum value of “air capacity” matches the internal capacity of the plastic bottle rocket 1 (for example, 1.5 L). The value to be

Next, the flight distance prediction procedure executed in step S3 of the flight distance prediction program (FIG. 5) will be described with reference to the flowchart of FIG.
First, in step S31, the value of the polytrol index “n” obtained by executing the program shown in FIG. 6 is recognized, and in the next step S32, the value of the PET bottle rocket 1 input to the computer 200 in advance is recognized. “Air resistance” and “effective opening area” effective when high-pressure water (liquid) or air (gas) is injected with respect to the opening of the injection nozzle 1A of the PET bottle rocket 1, and other injection conditions (for example, , The pressure inside the PET bottle rocket 1, the total mass when the PET bottle rocket 1 is fired, the mass of water, the launch angle, etc.) are recognized, and in step S33, these recognized values and the polytropic index “n” recognized in step S31 are detected. The flight distance of the plastic bottle rocket 1 is predicted based on the value “”.

  Here, the “air resistance” of the plastic bottle rocket 1 can be obtained by using a dropping device 40 shown in FIG. That is, the plastic bottle rocket 1 can be freely dropped from the height Hf, the actual drop time can be obtained, and the “air resistance” can be calculated based on these values. In the figure, 41 is a dropping device for freely dropping the plastic bottle rocket 1 at an arbitrary timing, and 42 in the figure is a sensor for detecting that the plastic bottle rocket 1 has landed. The time from the start of the drop until the sensor 42 detects that it has landed is the time taken for the PET bottle rocket 1 to actually fall after receiving the “air resistance” from the height Hf. By comparing the calculated value of the drop time in the ideal state based on the gravitational acceleration, the value of the “air resistance” can be easily obtained.

In determining the flight distance, the mass of water filled in the PET bottle rocket 1, the amount of air, the internal pressure, etc. are values that change over time, so the time from launch to arrival (landing) is the same. By dividing each unit time and calculating the flight distance of the PET bottle rocket 1 by accumulating the flight distance per unit time, it is possible to predict with high accuracy.
In this case, every time the unit time elapses, the “effective opening area” of the injection nozzle 1A is calculated each time. The “effective opening area” calculated every time the unit time elapses, the “air resistance” and the PET bottle rocket 1 are calculated. The flight distance (flight characteristics) can be calculated with high accuracy by the computer 200 by using the “polytropic index n”.

As for the “effective opening area” of the injection nozzle 1A, the flight distance is calculated on the assumption that it is “constant” during the flight time, while the flight distance when the plastic bottle rocket 1 is actually launched is calculated. A plurality of data is obtained, these two values are compared, an average value of the “effective opening area” is obtained, and the flight distance can be estimated with the average value of the “effective opening area”.
If the flight distance of the PET bottle rocket 1 is simply predicted using the correlation between the polytropic index “n” and “flight distance”, for example, as shown in the graph of FIG. For example, PET bottle rockets 1 where “n” is, for example, “1.2”, “1.3”, and “1.4” are prepared, and injection experiments are performed under the same conditions. By sampling each flight distance (180m, 165m, 160m in the example of FIG. 17), the flight distance when the politocorp index “n” is between these three values can be easily calculated by interpolation calculation. It can also be predicted.
Thus, by calculating in advance the polytropic index “n” that changes in accordance with the injection energy of the PET bottle rocket 1, it is possible to accurately and easily obtain the prediction of the flight distance of the PET bottle rocket 1. It becomes.

  As described above, according to this embodiment, the polytropic index “n” is acquired based on the actual measurement value θmax of the maximum rotation angle of the rotary bar 120 obtained by the measuring apparatus 100 and the calculated value θcal by the computer 200. Therefore, using the value of the polytropic index “n”, the flight distance (flight characteristics) of the PET bottle rocket 1 can be obtained easily and accurately.

In this embodiment, the computer 200 is repeatedly processed until the calculated value θcal matches the actual measurement value θmax. However, at the learning site, the value of “n” is increased or decreased each time. It may be performed artificially.
In this embodiment, the “plastic bottle rocket” used in school education has been described. However, a liquid (water in this embodiment) is injected into the interior, and the internal gas (in this embodiment) is set to a high pressure. In the case of a flying object that is launched by being jetted together with air), the flight characteristics (for example, flight distance) can be accurately predicted by the same procedure.

In this embodiment, the actual measurement value of the maximum rotation angle of the rotation bar 120 of the measurement apparatus 100 is electrically detected by the detection unit 150 and the signal is input to the computer 200 via the cable 160. For example, as shown in FIG. 4, a holder 120 </ b> C that can be fixed with a writing instrument (for example, a pencil) 60 inserted at the end of the rotating bar 120 is provided and rotated when the rotating bar 120 rotates. The maximum rotation angle θmax may be recorded by drawing a trajectory along which the holder 120 </ b> C portion of the bar 120 moves with the writing instrument 60.
In this case, the measured value θmax may be confirmed by the experimenter, and the value may be input to the computer 200 artificially. The computer 200 calculates the polytropic index n based on the input maximum rotation angle θmax and the calculated value θcal.

    In this embodiment, the “flight distance” has been described as the flight characteristic of the plastic bottle rocket (flying object) 1. However, if the flight characteristic depends on the injection energy, for example, the plastic bottle rocket (flying object) 1 The “impact force” when hitting the target object can be predicted in the same manner.

  The present invention can also be used for predicting the flight characteristics of other flying bodies that enclose the internal liquid or gas with high pressure and inject the liquid or gas to obtain power energy.

  1 is an overall configuration diagram of a measuring apparatus 100. FIG.   It is a figure which shows operation | movement of the measuring apparatus 100 at the time of discharge of the plastic bottle rocket 1. FIG.   It is a figure which shows the structure of the attaching part.   It is a figure which shows the rotation angle detection apparatus 150 structure.   It is a flowchart figure which shows the program for measuring a flight distance.   It is a flowchart figure which shows the program which acquires a polytropic index.   It is a flowchart figure which shows the program which acquires the outflow speed and outflow amount of the water in the PET bottle rocket.   It is a flowchart figure which shows the program which acquires the rotational torque and inertia moment of a rotation bar at the time of water injection.   It is a flowchart figure which shows the program which calculates the angular acceleration, angular velocity, and angle of the rotation bar 120 at the time of water injection.   It is a flowchart figure which shows the program which acquires the various parameters relevant to the air in the PET bottle rocket 1 at the time of water injection.   It is a flowchart figure which shows the program which acquires the outflow speed and outflow amount of the air in the PET bottle rocket.   It is a flowchart figure which shows the program which acquires the rotational torque and inertia moment of a rotation bar at the time of air injection.   It is a flowchart figure which shows the program which calculates the angular acceleration, angular velocity, and angle of the rotation bar 120 at the time of air injection.   It is a flowchart figure which shows the program which acquires the various parameters relevant to the air in the PET bottle rocket 1 at the time of air injection.   It is a flowchart of the program which performs the calculation process of flight distance.   It is a figure which shows the apparatus 40 for acquiring the air resistance of the PET bottle rocket.   It is a graph for acquiring flight distance by interpolation calculation.

1 PET bottle rocket (aircraft)
1A Injection nozzle 100 Measuring device 120 Rotating bar (Rotating body)
DESCRIPTION OF SYMBOLS 130 Attachment part 140 Adjustment part 141 Weight 150 Rotation angle detection apparatus 200 Computer

Claims (6)

An apparatus for measuring an injection energy of a flying object,
A main body provided with a rotation shaft;
One end is rotatably supported on the rotating shaft, and the other end is provided with a mounting portion to which the flying body is mounted;
An apparatus for measuring an ejection energy of a flying object, comprising: a detection unit that detects a maximum rotation angle when the rotating body rotates according to the ejection energy when the flying object is launched.   The said detection part outputs the detected maximum rotation angle of the rotary body as an electric signal, The flying body injection energy measuring apparatus of Claim 1 characterized by the above-mentioned.   The flying object has an injection nozzle, and a gas and a liquid pressurized to a predetermined pressure are enclosed in the flying object, and when the injection nozzle is opened, the gas or liquid is injected into the flying object. The propelling force is obtained by being jetted to the outside of the aircraft, and the flying energy jet energy measuring device according to claim 1 or 2.   The said flying body is a plastic bottle rocket, the said liquid is water, and the said gas is air, The injection energy measuring apparatus of the flying body of Claim 3 characterized by the above-mentioned. Recognizing a maximum rotation angle of the rotating body based on a signal from the detection unit according to claim 2;
Calculating the maximum rotation angle of the rotating body based on the outflow state of the liquid and gas inside the flying body, the rotating state of the rotating body, and the change state of the liquid and gas inside the flying body;
Obtaining a polytropic index of the flying object based on the recognized maximum rotation angle and the calculated maximum rotation angle;
And a step of acquiring a predicted value of the flight characteristic of the flying object based on the polytropic index. Recognizing the maximum rotation angle of the rotating body based on the signal from the detection unit according to claim 2;
Recognizing the air resistance of the flying object;
Recognizing the effective opening area of the jet nozzle of the flying object;
Recognizing at least the mass of liquid sealed inside the projectile, the pressure applied to the interior, and the launch angle of the projectile;
Calculating the maximum rotation angle of the rotating body based on the outflow state of the liquid and gas inside the flying body, the rotating state of the rotating body, and the change state of the liquid and gas inside the flying body;
Obtaining a polytropic index of the flying object based on the recognized maximum rotation angle and the calculated maximum rotation angle;
A flight distance acquisition program comprising: calculating flight characteristics of the flying object based on the polytropic index, the recognized air resistance, and the recognized effective opening area of the injection nozzle.

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