Rocket car strategy

[SomptingGuy]

My company runs a rocket car race on or around 5th November most years. Contestants build small cars to be powered by one standard rocket (firework size). Longest distance travelled wins.

My question: Why is it always the lighter cars that win? I know they have less friction, but they win by a country mile. Is there any inherent advantage to be had by getting off the line fast - i.e. does a moving vehicle somehow extract more of the available rocket power than a stationary one?

 

[Jabberwocky]

Without delving into the maths as some have, it still feels pretty simple to me. If the rocket motor provides equal output to all cars, you'll have light cars accelerating faster than the heavy cars.

Both coast to a stop after the same amount of time (same rocket) and then the rest of the distance involves constant losses to friction, both through wheels and air.

If the light car is moving faster than the heavy car at flameout, it has that much farther to travel before losing everything to the wheel friction.

Assuming of course the wheels and axle bearings are anything like the Hot Wheels I used to play with.

If you had a magnetic bearing maybe you'd win?

 

[Fabrico]

vehicle 1 assumptions:
mass (kg) 0.1
density (kg/m3) 1.2
frontal area (m^2) 4.00E-03
Cd 0.35
Constant Thrust (N) 1
Burn Duration (s) 3
Crr (N/kg) 0.3

at zero seconds, the state of vehicle 1 is:
Time 0
thrust (N) 1
acceleration (m/s2) 10
velocity (m/s) 0
distance (m) 0
Rocket Work (J) 0
vehicle KE (J) 0
rolling res. (N) 0
aero drag (N) 0
rolling loss (J) 0
drag loss (J) 0

at 0.01 seconds, the state of vehicle 1 is:
Time 0.01
thrust (N) 1
acceleration (m/s2) 9.699920475
velocity (m/s) 0.097299773
distance (m) 0.000487849
cumulative Rocket Work (J) 0.000487849
vehicle KE (J) 0.000473362
rolling res. (N) -0.03
aero drag (N) -7.95249E-06
cumulative rolling loss (J) -1.46355E-05
cumulative drag loss (J) -2.1977E-09

The vehicle continues to accelerate, and reaches max velocity at flame-out:
Time 3.001
thrust (N) 0
acceleration (m/s2) -4.97952904
velocity (m/s) 23.60268608
distance (m) 39.19699735
Rocket Work (J) 39.17339717
vehicle KE (J) 27.85433952
rolling res. (N) -0.03
aero drag (N) -0.467952904
rolling loss (J) -1.17590992
drag loss (J) -10.17411135

the vehicle slows to a stop, finally reaching 0 m/s much later:
Time 29.351
thrust (N) 0
acceleration (m/s2) -1.14926E-10
velocity (m/s) -0.000116969
distance (m) 206.4020208
Rocket Work (J) 39.17339717
vehicle KE (J) 6.84083E-10
rolling res. (N) 0
aero drag (N) -1.14926E-11
rolling loss (J) -6.192060622
drag loss (J) -33.00493688

forgive the fact that the cumulative losses are slightly different than the total work input - it was a quick-and-dirty spreadsheet calc and I didn't spend much time thinking about changes between the timesteps. 0.06% error is probably okay.

Vehicle 2:
mass (kg) 0.3
density (kg/m3) 1.2
frontal area (m^2) 4.00E-03
Cd 0.35
Thrust (N) 1
Burn Duration (s) 3
Crr (N/kg) 0.3

@Time=0.01s
Time 0.01
thrust (N) 1
acceleration (m/s2) 3.033330706
velocity (m/s) 0.030633326
distance (m) 0.000154517
Rocket Work (J) 0.000154517
vehicle KE (J) 0.00014076
rolling res. (N) -0.09
aero drag (N) -7.88257E-07
rolling loss (J) -1.39065E-05
drag loss (J) -6.89924E-11

@max velocity:
Time 3.001
thrust (N) 0
acceleration (m/s2) -0.520703115
velocity (m/s) 8.878205952
distance (m) 13.48942788
Rocket Work (J) 13.48055108
vehicle KE (J) 11.82338114
rolling res. (N) -0.09
aero drag (N) -0.066210934
rolling loss (J) -1.214048509
drag loss (J) -0.452390269

@final stop:
Time 27.446
thrust (N) 0
acceleration (m/s2) -0.300000065
velocity (m/s) 0.004816143
distance (m) 111.9517007
Rocket Work (J) 13.48055108
vehicle KE (J) 3.47928E-06
rolling res. (N) -0.09
aero drag (N) -1.9484E-08
rolling loss (J) -10.07565306
drag loss (J) -3.413771489
...
should note:
mass (kg) - total mass of vehicle

density (kg/m3) - density of air

frontal area (m^2) - (of vehicle)

Cd - drag coeff. of vehicle

Thrust (N) - thrust delivered by rocket (constant) during burn

Burn Duration (s) - duration of rocket burn

Crr (N/kg) - ratio of rolling resistance to mass (assuming crappy wheels and bearings)

Time - time in seconds since start of calc

thrust (N) - thrust delivered by rocket over preceding timestep

acceleration (m/s2) - acceleration of vehicle over preceding timestep (constant per step)

velocity (m/s) - velocity of vehicle at end of preceding timestep

distance (m) - distance travelled at end of preceding timestep

Rocket Work (J) - cumulative work done by the rocket on the car since the start of the calculation

vehicle KE (J) - approximate kinetic energy of the vehicle at the end of the preceding timestep (0.5mV2) - excluding rotational KE of the wheels+axles

rolling res. (N) - rolling resistance experienced by the vehicle at the end of the preceding timestep (Crr*m)

aero drag (N) - aero drag experienced by the vehicle at the end of the preceding timestep (0.5*density*Cd*A*V2)

rolling loss (J) - cumulative energy lost to rolling resistance since the beginning of the calc

drag loss (J) - cumulative energy lost to aero drag since the beginning of the calc

Hmmm, which one is better; science based on assumptions or assumptions based on science? I'll take the latter.

 

[ivymike]

...still waiting for something more than hot air. what "science" are you referring to? where are your cadillac and beetle?

 

[Fabrico]

ivymike, you seem to be an arguement waiting to happen. But more than anything else, you appear to be arguing with youself. Perhaps I am stupid beyond belief, but I don't think I am alone in not quite knowing what your point is.

My original reference was to the OP who does not appear, or try to appear, to be a rocket scientist.

I, and apparently a few others, need nothing more than the simple hot air already given. The lighter car accelerates easier. It rolls easier. It coasts farther. It goes farther. It wins the race. I will challange your lengthy equations when you convince me otherwise.

This analogy might be tough for you, but if I had to push a car through the quarter mile, and the choice was between a Cadillac or a Beetle, I know which one I would choose. And I would again reserve the right to not use math in my decision.

 

[globi5]

Btw the impulse equation works as well as the energy/power equation. (So SomptingGuy's co-workers are not wrong.)

The rocket equation is based on the impulse law and it says:
v_max = v_fuel * ln((mass_empty+mass_fuel)/mass_empty)

So the lighter the vehicle the higher v_max and thus the farther the vehicle travels.

Or if you were to release all fuel at once you can use the general impulse equation and get:

v_rocket = mass_fuel/mass_empty * v_fuel

 

[Jabberwocky]

Self-edit

Please replace "coast to a stop" with "lose thrust" in my above post.

Forget all the air-blowing anyways, why hasn't anybody posted time-trial results of their custom rocket cars yet? Does the car have to stay on a track or can it go airborne?

I think we could have some fun with downforce and stability concerns - a Star to the first person to come up with a landfoil (what I envision as a rocket with a small trailing set of wheels/skids so it still counts as being on the ground).

 

[SomptingGuy]

Will report back after the race.

 

[Pud]

You might try try this for a complete "headcase" solution...

http://aardvark.co.nz/pjet/gokart.htm

Cheers

Harry

 

[Rob45]

If the weight weren't important, an Expedition would go as far on a gallon of gas as a Prius.

 

[bvanhiel]

Rob45,

While the obvious solution happens to be correct, the reason behind it is not so simple.

If it were an equal energy situation, such as if the cars were all powered by the same spring or the same gallon of gas, then I think an argument could be made that the heavier vehicle would travel more efficiently due to less drag encountered at its lower top speed. This would balance against increased rolling resistance, and you could calculate an optimal car weight. For example, which goes farther when you shoot it out of a gun: a feather or a bullet?

The difference in this situation is the nature of the rocket. The rocket produces a fixed force, so you can capture more of the power produced by the rocket the faster you are going. There would be no optimal weight, as the lightest car would always win.

I think it's an interesting problem.

-b

 

[SomptingGuy]

As promised, a brief report...

The rockets this year clearly had higher and longer thrust than in years past, to the point where structural integrity and directional stability were probably more important than any energy balance calcs. The winner (light and strong, with DIY solid tyres) topped 65m and was still bombing along at a high rate of knots when it left the track and stopped in the grass.