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Ploting trajectory, including air resistance.

  1. Jan 21, 2007 #1
    I am trying to plot the trajectory of a projectile. I found formulas for finding the drag force, but it only gives me the drag force at an impossibly short interval of time, i need it to affect the trajectory of the projectile threw out it's path. The projectile is also affected by gravity. If anyone could help me out here, either by giving me a different drag formula or even better, in the form of y=, that would be great.

    This formula is going into a program to calculate and graph the path of projectiles fired out of compressed air powered spud guns.
  2. jcsd
  3. Jan 21, 2007 #2
    If you want the most accurate results, you have to know how to use a computer to approximate differential equations. I have some code in Mathematica, but I doubt you use that.

    If programming is not an option you will have to find a software that does this for you (of which I am sure their are many). The problem is that realistic modelling of air resistance involves nonlinear differential equations, and in this case the equations do not have a closed from solution (a formula y = ).

    If you feel you must resort to pen and paper methods, then certain approximations can be made to get you a "y =" that partially models air resistance. Depending on your desired accuracy (i.e. pen-paper is good enough unless you are going to measure wind) this could be viable.
  4. Jan 21, 2007 #3
    No, computers is how I intend to do this. I don't know a thing about differential equations, but I have been programming for years. I am making a program for doing it. I made one already that calculates the muzzle velocity and the maximum height of the projectile fired straight up in a vacuum, but it is useless to me, it needs air resistance.
  5. Jan 21, 2007 #4


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  6. Jan 21, 2007 #5
    That didn't include drag and I am not using Excel, it will be an executable, written in C++. I know the formula for drag, but drag changes based on velocity, and the velocity is constantly changing.
    Last edited: Jan 21, 2007
  7. Jan 21, 2007 #6
    Why was my thread moved into the homework section? This project is not in any way school related.
    Last edited: Jan 21, 2007
  8. Jan 21, 2007 #7
    I wouldn't have thought this was related to a homework problem... especially if you don't know anything about differential equations! The drag force depends on the shape of an object, its speed, and properties of the object and the air. The higher the speed, the higher the drag force; I'm sure you realize this at this point. However, there are several models for drag force, one is that the drag force is proportional to the velocity. Another common model is that the drag force is proportional to the velocity squared. i.e. F=-cv or F=-cv^2, where c is a positive constant dependent on the properties of your projectile. You're in luck! If you assume the drag force is proportional to the velocity, I think that leads to a first order linear differential equation which can be solved for the velocity as a function of time... sort of. Unfortunately, that may not be the correct model for a potato flying through the air. Equally unfortunate is that you're probably going to need experimental data in order to find what the constant is.

    There's a reason that intro physics courses say "ignore air resistance" or "ignore drag forces" - the mathematics get quite complicated!
  9. Jun 25, 2008 #8
    I am also trying to do somthing similar, I have learned how to solve differential equations in class, I am just trying to set up the differential equation, (I took calc but trig bassed physics) I have the air density formula, the force of drag formula, and basic contants (Drag coeficiant, frontal area, initial velocity, mass of projectile etc..) I need with the projectile I am using. So far I know that the velocity of time would be somthing like this V(t) = Vi - (Force of drag/mass of projectile)*t. Unless I have it wrong please correct me. No the problem is that Force of drag (Fd) requires the V(t) to calculate Fd. Ie V(t) = Vi - (905.8656 - ((.5 * p * (V(t)^2) * (4.56036731 × 10-5 ) *.507) / .0116638038)t). So I know I need calc here its just setting it up is getting me. Anyways I think this is my final formula sombody please check it I just tried solving using substitution but then again I think I nuked it, 912952.4078072/(p*time) = V(t)

    Anyways one other side note, I used Vi as a constant but I will put as inputed variable in to the program. I am debating on writing it as Ti-Basic (for 83/84 most likley) or as a .exe. In anycase I will post it when I am done onto the forums. If i do .exe I will have it input any mass, frontal area, and drag coeficient as a variable, also tied into the program will be manual entering of forcasted air pressure, humidity, and temperature, to further calculate the velocity of time t.

    p= density of fluid (air) for which I have a formula it is in kg/m^3 (I can take care of this for the most part, I will just leave it as a variable, I have a seperate program all set for that bassed on temp and measured pressure and humidity. (takes altitude out of the equation)
    V(t)= Velocity of time
    Vi = Initial velocity (will be as variable in the program) = 905.8656 m/s
    Mass of projectile if needed = 11.6638grams

    Side note: I realized not everything has correct number of significant digits, I am going by conversions and ctrl + C....Ctrl + V for numbers, it should get me close enough to where the program will round to the nearest m/s anyhow.
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