Calculating Constant Thrust for Jet-Powered Drag Car in Vehicle Dynamics Class

[dochalladay32]

I'm a math guy taking engineering classes more or less for fun, so some of the stuff I should know I probably missed in a basic dynamics class. I feel really dumb that I can't figure this out.

I'm in a vehicle dynamics class and I have to calculate the constant thrust T for the following situation:

I have a jet-powered drag car that weighs 3220 lbs and goes from 0 to 260 mph in a quarter mile. The drag force is D = 0.006*v^2, D is in lbs and v is in ft/s. We are to neglect the tire rolling resistance so only T and D affect the movement of the car. We are also told to use 0.002378 slug/ft^3 for air density. For some reason, I have no clue how to calculate the thrust in this case. I'm used to mass flow rates and exhaust velocities.

What am I missing that presumably makes this problem so easy? Thanks for anything you guys can offer.

 

[PhanthomJay]

I am not sure why you were given the air density since it is already factored into your formula for D (assuming it is given correctly).

The acceleration is not constant since the drag force is not constant. You have to solve the differential equation formulated from Newton's 2nd law, where a = dv/dt or a = d^2x/dt^2. Unless your good at calculus, the solution is a bit messy. Being a math guy, I'm sure you can solve it better than I. What does Newton 2 tell you about the equation to use to solve for the Thrust?

 

[dochalladay32]

The air density threw me off as well, because there is no way to get A_f and C_d, so it's rather pointless here. That's why I was thinking there had to be some trick to what he was asking, because it looks excessive.

What you mentioned was what I was trying to do, but he seems to think that we should be able to find the value of T rather easily, and I'm just not seeing that. Thanks for confirming what I had in mind and I'll just go with it and maybe it'll come in class next week.

I am solving the differential equation T - 0.006v^2 = 100*dv/dt for v with initial velocity of 0. That will give me motion curves I need, which is another part of the homework. I'll take it from here and hopefully this will lead to an answer for T. Doesn't seem like it is going to be constant though, but it's late so maybe I just can't see it yet.

Thanks a lot!

 

[SteamKing]

T is constant by definition. You have to determine T knowing that vo = 0, vf = 260 mph, and sf-so = 1320 ft. You DE can be solved by separation of variables or by using one of the numerical techniques for first order ODEs.

 

[dochalladay32]

Thanks for the help guys. Took some work doing the integrals, but I got answers that all make sense. Takes 5956 lbs of thrust to get the car up to that speed in a quarter mile. Everything checks out. Now I have to do it again without the drag, but the integrals will be much nicer this time. Thanks again!