Originally posted by rocketsonly
Does anyone know any simple principles of trajectory?
I do know you aren't allowed to tilt the launch rod more than 30 degrees from perpendicular.
One of my previous science teachers asked if my TARC team could launch some rockets on Veterans day (November 11). We were thinking of using some G's and tiliting the rail so that the rocket would go over to this gigantic piece of land consisting of a football field, a 400m track (and field), and a soccer field side by side.
Is this a good idea? Bad idea? Comments?
Thanks.
Lookout, Rocketguts is going Hollywood!
Sure, you can do it. Any scientific calculator has the right buttons. Which ones to push comes from trigonometry.
This is going to a be perfect-world, Newtonian, Galilean, physics class description. We'll deal with reality later.
A rocket, having no lift, follows a ballistic trajectory. In the simplest case, a falling object accelerates at 16 feet per second squared -- it just falls. If that object also had speed relative to a point on the ground -- forward speed -- that would continue. Gravity doesn't care if something's dropped or moving forwards. A bullet does this. Once fired, it may be going forwards real fast, but it drops to the ground at the same time it would have if you'd dropped it from your hand at the same height.
If the object has upward speed, gravity still acts exactly the same way. The object "falls" as long as it's not being pushed up. If it's travelling upwards but not under power, this means that the acceleration due to gravity is simply a subtraction in its upwards speed, at the same rate: 16 ft/sec^2. Until that becomes zero, of course, then it's adding and down.
A rocket gets pushed up by thrust. As long as the thrust pushes, the above doesn't apply. When the thrust stops, though, gravity takes over. The best way to see this is to use Rocsim, SpaceCad or even just the rocket simulators on EMRR and get a point by point prediction for any old rocket. Thrust accelerates it, when that stops the upward acceleration switches to gravity powered decelleration, it peaks and starts to fall. If you fire a rocket straight up, it follows its boost phase and then "falls", even if it's while it's still rising.
If you fire at an angle, the amount of speed it gets remains the same as if you'd fired it straight up. Hopwever, the amount of speed that goes to "up" and the amount that goes to "forwards" will depend on the angle. The flight path is the hypotenuse of a right triangle. You have that length from the alitude prediction, and you have the adjacent angle. Now it's time to get out the trig book and calculate the length of the other two sides. Their length, divided by the boost time, gives you the speed.
Ignore the forwards part for now. Take the upwards part and start subtracting speed until it reaches zero, then start adding downwards speed. Keep track of how much "up" is left, until that amount is zero. The Eagle has landed. Hard.
The forwards speed, well you know how much it gets. Just assume it keeps all that. Now you can calculate the forwards speed just like the upwards and add up how much you get if it travels forwards until the zero altitude time you just calculated. Multiply speed times time and you've got downrange distance.
We haven't figured in airflow drag. The simulators do. Trust them.
So, you come up with flight path described by a diagonal line at an angle to the ground which is your launch angle. Starting from there, your trajectory becomes a parabola. That continues until it hits the ground, or something.
Or Something: We don't want to hit the ground yet. We have a delay and ejection. So, follow the path only as far as the boost time plus delay. At that time, the chute comes out, and it comes down in a completely unscientific and realistic manner. Descent can be calculated by the descent calculators on EMRR (love that "tools" section). Now you've got a diagonal line, mostly up, some forwards, then a parabola, don't worry about the up, still forwards, until a certain point X amount downrange and Y amount altitude. The path after that depends upon the wind speed, chute efficiency, weight, the attractive field of Rocket Eating Trees, etc.
If you want to spot land these, calculate the trajectory as above (for different launch angles and/or distances from the landing area. With a little trig and the data from a flight predictor, you can draw it out.
My recommendation is to do this all the way to the ground, adjust your angle so that a lawn dart would land dead center of the landing area, and use as long a delay as possible as long as it's not after your altitude prediction says zero. And use real tough recovery gear. The higher the ejection, the more your landing will be at the whim of the Rocket Ghods. I say dead center because if the chute works, it'll land closer which is a good thing, and if it lawn darts, you've got maximum safety zone, a major consideration for public displays. T
To be on the safe side, do the calculations with zero, 5 10 and 15 MPH additions to the forwards speed, and what angle you have to use to hit dead center. On the day of launch, check the wind speed and direction and adjust your launch angle accordingly, including even a left/right component if necessary.
And since you're doing this in public and want it to look professional, after calculating everything, go practice. Because it's scientific, and engineeringistical, and hey, you've got an excuse to launch more rockets.
Veteran's Day? Plenty of time. I know a amateur mad rocket scientist verteran who could help out. He's got a caulculator. As you can probably tell from a few vague points above, he doesn't have a trig book. I bet the school does though.
