CN111310367A - Method for calculating jet flow compensation angle of automatic fire monitor - Google Patents
Method for calculating jet flow compensation angle of automatic fire monitor Download PDFInfo
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- CN111310367A CN111310367A CN202010310281.6A CN202010310281A CN111310367A CN 111310367 A CN111310367 A CN 111310367A CN 202010310281 A CN202010310281 A CN 202010310281A CN 111310367 A CN111310367 A CN 111310367A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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Abstract
The invention relates to a method for calculating an automatic fire monitor jet flow compensation angle. In order to overcome the defects that the traditional air resistance and speed proportional method has too close drop points and the air resistance and speed square proportional method has no analytic solution, the invention adopts different resistance model modes in the horizontal direction and the vertical direction, namely, a resistance and speed square proportional model is adopted horizontally, and a resistance and speed proportional model is adopted vertically. The invention provides a motion equation set which meets the conditions, and a trajectory equation and a jet flow compensation angle are obtained by solving. The automatic fire monitor can calculate the compensation angle in real time according to the formula so as to achieve the purpose of accurately extinguishing fire by jet flow.
Description
Technical Field
The invention relates to a jet flow track calculation technology, in particular to a method for calculating an automatic fire monitor jet flow initial pitch angle by giving a jet flow floor point.
Background
After the fire monitor is positioned to the ignition point, whether the jet flow can accurately hit the ignition point is the key for fire extinguishing. Because the jet flow is influenced by gravity and air resistance, the track in the air is not a straight line, and therefore the initial pitch angle needs to be compensated to achieve the aim that the landing point is consistent with the target point.
The jet motion in the air can be seen as water mass motion, similar to projectile motion. Therefore, the existing method can be divided into two forms of analytic solution and numerical solution according to the form of ballistic motion equation solution. In the first category, the motion equation resulting in an analytic solution generally employs a motion model in which the resistance is proportional to the velocity.
The project design bulletin (title: model of jet motion trail and positioning compensation method of fire water monitor), author: Chen scholar, Yangming, date: 2016 year 6, page number: 558-. However, at this setting, the authors have verified that the jet landing point is close to the center of the source of the fire, causing a deviation. This indicates that the air resistance is greater than the established model. Therefore, the method of segmented correction compensation is further adopted to increase the initial pitch angle according to the distance of the fire source so as to meet the actual requirement.
The fire-fighting science and technology (subject: water jet trajectory fitting equation of fire monitor, author: Wanfeng, Chengxiang, etc., date: 2007 6, page number: 656-657) also adopts a model with proportional resistance and speed. The conclusion is basically consistent, namely the falling point is close and the error is large. To compensate, the authors again adjusted the equation coefficients further in a fitting manner.
Chinese patent (patent application No. 201310745715 'jet pitch angle calculation method for automatic tracking and positioning jet extinguishing device') adopts a calculation model with air resistance proportional to speed. The formula for calculating the fire extinguishing jet pitching angle FireA in the text is consistent with the formula (8) in the thesis fire water monitor jet motion track model and positioning compensation method (y is 0, namely the horizontal plane drop point); the method is the same as the formula (8) in the thesis 'fire monitor water jet trajectory fitting equation' (three-order small terms in series expansion need to be omitted and the angle needs to be calculated).
Models where air resistance is proportional to velocity do not allow accurate calculation of the water drop point because the air resistance contribution is underestimated. Therefore, the second category of methods represented by numerical solutions, which employ a resistance proportional to the square of the velocity, all better fit the actual jet trajectory.
The Journal of Heat and Fluid Flow (title: "computer of the objects of large water jets", author: Hatton A P et., date: volume 2, 1985, page number: 137-
Description of the jetThe relationship between the air resistance f and the speed v, wherein s is the length of the jet flow arc, and k and b are two undetermined coefficients. It can be seen that the air resistance is modeled as being proportional to the square of the velocity.
The mechanical engineering newspaper (topic: "fire water monitor jet flow track theoretical model considering pitch angle", author: Minyonglin et al, date: 2011 volume 47, page number: 134-
. Wherein the content of the first and second substances,
the pitch angle is, a and b are undetermined coefficients, and t is time. The method saves the trouble of calculating the arc length s. The thesis verifies that the model better simulates the actual jet trajectory curve without additional angle compensation or coefficient adjustment.
The general paper of Shanghai university of transportation (topic: "study of fire monitor jet trajectory", author: Sunjian, date: 2008) gives a resistance calculation formula as
. Wherein k is an air resistance coefficient,
for air density, A (x) is a function of jet cross-sectional area variation. Similarly, the resistance is in direct proportion to the square of the speed, and the experimental conformity degree is better.
Since the resistance is proportional to the square of the velocity, the motion equation is a second-order quadratic differential equation, and an analytic solution cannot be generally obtained. Therefore, such methods all use numerical calculation methods such as euler or longge stoke to repeatedly and iteratively solve. For an automatic fire monitor system, the position is known and the compensation angle is sought. For any given position, the numerical solution method needs to repeatedly bring different initial values of the compensation angle into an iterative formula, and finally the compensation angle obtained by calculation when the landing point is closest to the known position is taken as a final result. The calculation process is complicated and complicated. The automatic fire monitor system based on the single chip microcomputer and high in real-time requirement is undoubtedly unacceptable.
Therefore, for the two methods, the analytical solution has the advantages that a specific compensation angle calculation equation can be given, and the defects that the calculated compensation angle is small and the jet flow landing point is close; the numerical solution has the advantages that the calculation of the floor point is more accurate, and the defects that the calculation is complex, a clear calculation formula cannot be given, and the practical application is not facilitated.
In summary, from the practical point of view, for an automatic fire monitor system, the compensation angle must be given in formula form due to the real-time requirement. Therefore, how to give more accurate formula expression in the form of analytical solution is an urgent need for practical application and is also the main content of the present invention.
Disclosure of Invention
Aiming at the existing problems, the invention provides a calculation method of the jet flow compensation angle, which effectively considers the air resistance influence and gives the result in an analytic solution form.
The invention has the following beneficial effects and advantages:
1. the method for calculating the jet flow compensation angle of the automatic fire monitor can solve the problem that the current analytic solution method is insufficient in air resistance estimation, so that the water flow landing point is close to the ground point;
2. the calculation method of the jet flow compensation angle of the automatic fire monitor provided by the invention has the advantages of few parameters, simple calculation and no need of iteration, and is suitable for real-time calculation of a singlechip system of the automatic fire monitor.
Drawings
FIG. 1 is a schematic view of an application scenario of an automatic fire monitor jet in the method of the present invention;
FIG. 2 is a schematic diagram of the force exerted by the jet in the air in the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
FIG. 1 is a schematic diagram showing a jet flow application scene of an automatic fire monitor in the method, wherein the fire monitor is located at a point G on a y axis in an x-y coordinate system, the known installation height is h, a fire point is located at a point F on the x axis, the known coordinates are (x, 0) & α are fire monitor jet flow pitch angles (or called compensation angles), a pitch angle α takes the point G as a circle center, an x axis parallel line is a fixed edge, a movable edge is overlapped with a fire monitor nozzle, and the counterclockwise direction is the positive direction, and as shown in the figure, when the fire monitor shoots water with α as the jet flow pitch angle, a water flow floor point is F.
Fig. 2 is a schematic diagram of the force of the jet in the air. In the figure v0Is the initial velocity of jet flow, m is the mass of water mass of jet flow, g is the gravity acceleration, k is the air resistance coefficient, f is the air resistance, v is the speed of water mass in the air, is tangent to the motion trajectory line, and can be decomposed into horizontal and vertical velocity components vxAnd vy。
The air resistance of the water mass moving in the air can be decomposed into horizontal and vertical directions. The horizontal direction is the main travel direction of water spraying of the fire monitor, the water mass speed is high, and the influence of air resistance is large; the stroke of the water mass in the vertical direction is short, the speed is slow, and the resistance of the water mass to air is relatively weak.
It is known from the foregoing that the compensation angle obtained by using the resistance model in which the air resistance is proportional to the square of the velocity is more accurate than that obtained by using the resistance model in which the air resistance is proportional to the velocity. However, if a velocity squared proportional resistance model is used in both the horizontal and vertical directions, the equation of motion will not be computationally an analytical solution. Therefore, we get the second place, and adopt a resistance model proportional to the speed in the vertical direction with relatively slow speed and relatively short stroke; and in the horizontal direction with higher speed and longer stroke, a resistance model which is in direct proportion to the square of the speed is adopted.
Under the above premise, according to newton's second law, the motion equation of the water mass in the air can be expressed as:
solving the equation of motion in the horizontal direction requires the introduction of a horizontal velocity component
The horizontal equation of motion becomes:
has an initial value
To obtain the following solution:
and (3) carrying in an original motion equation:
there are initial values:
obtaining by solution:
the vertical motion equation has an initial value:
directly obtaining:
thus, the solution to the jet equation of motion is:
the equation set eliminates the variable t, resulting in:
namely the jet trajectory equation.
Will be provided with
Taylor expansion yields an approximate expression:
. Here, the second order small term is ignored and is substituted into the trajectory equation to obtain:
then will be
Taylor expansion yields an approximate expression:
. The third order small term is omitted here. Substituting the trajectory equation to obtain:
namely the jet flow trajectory equation obtained after simplification.
Further, unifying the trigonometric function into a tangent function, the above equation becomes:
further solution to pitch angle
Function of (c):
when the water mass falls to the ground, the water mass meets the requirements
Additionally provided with
The above formula becomes:
to ensure
The positive and negative terms are taken as the positive part and the negative part in the original formula, so that the relation between the pitch angle and the distance when the water mass falls to the ground is as follows:
therefore, given the installation height h and the displacement x of the landing point, the jet flow compensation angle can be calculated according to the formula
。
Claims (4)
1. A method for calculating the jet flow compensation angle of an automatic fire monitor is characterized by comprising the following steps: for the horizontal direction, a resistance model with air resistance in direct proportion to the square of the speed is adopted; for the vertical direction, a resistance model is used in which the air resistance is proportional to the speed.
2. A method for calculating the jet flow compensation angle of an automatic fire monitor is characterized by comprising the following steps: the jet motion equation can be described by the following equation:
wherein h is the installation height of the fire monitor, k is the air resistance coefficient, m is the mass of the water mass, g is the acceleration of gravity, v0The initial jet velocity is α, the initial jet angle is α, and x and y are the horizontal and vertical coordinates of the jet water mass respectively.
3. A method for calculating the jet flow compensation angle of an automatic fire monitor is characterized by comprising the following steps: the jet trajectory equation can be described by the following equation:
4. a method for calculating the jet flow compensation angle of an automatic fire monitor is characterized by comprising the following steps: the jet initial firing compensation angle can be described by the following equation:
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112923791A (en) * | 2021-01-21 | 2021-06-08 | 武汉科技大学 | Method for hitting target by jet device on moving carrier |
| CN114522367A (en) * | 2022-01-21 | 2022-05-24 | 天津博迈科海洋工程有限公司 | Rapid and accurate fire extinguishing method for automatic foam fire extinguishing vehicle of ocean platform |
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| EP2956344A1 (en) * | 2013-02-14 | 2015-12-23 | Scania CV AB | A method for managing parameters that influence the driving resistance |
| CN103217270A (en) * | 2013-04-17 | 2013-07-24 | 中南大学 | Dynamic model method for measuring tunnel air resistance coefficient of high speed train and application thereof |
| CN108939369A (en) * | 2018-05-25 | 2018-12-07 | 上海工程技术大学 | A kind of determination method for fire water monitor jet stream drop point |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112923791A (en) * | 2021-01-21 | 2021-06-08 | 武汉科技大学 | Method for hitting target by jet device on moving carrier |
| CN112923791B (en) * | 2021-01-21 | 2022-12-02 | 武汉科技大学 | Method for hitting target by jet device on moving carrier |
| CN114522367A (en) * | 2022-01-21 | 2022-05-24 | 天津博迈科海洋工程有限公司 | Rapid and accurate fire extinguishing method for automatic foam fire extinguishing vehicle of ocean platform |
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