Horizontal distance calculations

[dharak1]

The thread title is pretty vague so let me add on to that.

Lets say I have a model rocket with a max apogee of 300m, how would I calculate how far it would go horizontally if shot off at a 45 degree angle for maximum distance. We'll assume windspeed is zero but does air resistance have a different effect on the rocket if it isn't completely vertical. We can leave the parachute out too. I'd appreciate help with this, thank you in advance.

[Bill Phil]

Okay, there's many ways to do this. I've used the Euler method in a heavily simplified cannon ball FORTRAN program, which can output to excel and graph the path (awesome, to me).

But there are some pretty accurate methods, but I'm no expert on them. I'm afraid you'll need other members, or a lot of googling.

[Steel]

3 hours ago, dharak1 said:

The thread title is pretty vague so let me add on to that.

Lets say I have a model rocket with a max apogee of 300m, how would I calculate how far it would go horizontally if shot off at a 45 degree angle for maximum distance. We'll assume windspeed is zero but does air resistance have a different effect on the rocket if it isn't completely vertical. We can leave the parachute out too. I'd appreciate help with this, thank you in advance.

First a little correction, 45 degrees only gets you your max distance when air resistance is neglected, when you take it into account the max distance will be obtained with an angle lower than 45 degrees... assuming constant air density (which is fine for 300m). 

Also is the rocket's apogee if it goes straight up or is it when it's launched at 45 degrees?

Air resistance can be assumed to be only proportional to the speed of the rocket, it should not vary depending on the angle of the rocket in this situation.

The best way then to calculate this is to look up the equations of motion for projectile motion with air resistance and then solve them. There are many way to solve them, the Euler method as mentioned above is one of the simpler ways (and will be more than accurate enough for the sort of calculation you have in mind) but there are many more.

Edited January 4, 2016 by Steel

[YNM]

You'll also need to factor in that you've a specific burn time (the time the engine's on) and wind conditions. The last can make huuge difference once the rocket is fully empty. Euler method comes to mind, but I'm no coder to actually code that.

[Steel]

1 hour ago, Bill Phil said:

 

Quote

You'll also need to factor in that you've a specific burn time (the time the engine's on) and wind conditions. The last can make huuge difference once the rocket is fully empty. Euler method comes to mind, but I'm no coder to actually code that.

Yeah it's going to depend on how you want to model your rocket. If you want a simple option you can estimate the launch as instantly giving your rocket an initial velocity and then going from there, if you want to actually model the rocket as a rocket then that's another layer of complexity to add with force being applied by the engine and the mass of the rocket getting lower with time.

If you wanted to add in the effect of the wind then there's another layer, as you need to calculate the force on the rocket by the wind depending on how the rocket is oriented into the wind.

You can essentially make this as simple or complicated as you want.

Edited January 4, 2016 by Steel

[B787_300]

Honnestly the easiest way would be to treat the rocket as a point mass and then use the basic kinematic equations.  if you want something more precise that takes into account parachutes wind speed and direction then you would want to use a program like rocksim (more accurate, but costs $$) or openRocket (free, not as good)

[K^2]

Without air resistance and with short burn time (long coast time), maximum distance traveled when fired at 45° angle is twice the maximum height achieved when fired straight up. However, that's hardly reasonable assumption for a model rocket. Unfortunately, there is no formula you can simply plug this into to get the distance. Even if we ignore the engine thrust profile, and you simply shoot model rocket from a slingshot, air resistance is significant, and there is no analytic solution for ballistic trajectory with drag.

That means, the only thing you can do is plug the numbers into a computer model and run a simulation. Quadratic drag with constant drag coefficient gives reasonable approximation for a model rocket. Drag coefficient can be acquired by simply playing with the number until you get correct altitude for the given rocket motor. Of course, that assumes a known thrust profile, which you can usually get from rocket motor's manufacturer.