Solve Solar Drag Race Model Equation

[Jolly Green Tractor]

I am working on a model of a solar powered drag race.

The race: 250 meters, no incline, initial velocity = 0.

Classical physics gives us the following equations (ignores aero and rolling drag and wheel rotation):

Velocity as a function of time V = (2Pt/M)^.5
P = power, M = mass

Distance as a function of time d = (2/3)((2P/M)^.5)t^(1.5)

Time to travel x distance t = ((1.5d)^(2/3))(M/2P)^1/3


But of course we do lose power to aerodynamic drag forces

Pa = .5rCdAV^3 (r = air density, Cd = aero drag coef., A = frontal area)

and rolling drag at the wheels

Pr = CrMV (Cr = rolling drag coef.)

and wheel rotation

Pw = FwV^3 (Fw = wheel rotational factor)


So if our inertial power equals our power in, Pi (from the solar panel) minus our power lost to friction (aero, rolling, wheel rotation), then our velocity equation becomes:

V = (2((Pi-(.5rCdAV^3)-(CrMV)-(FwV^3))t)/M)^.5

I need help solving this equation. I have approximated the solution by chopping the race up into small pieces and solving iteratively, but I would rather do it right.

 

[jaap de vries]

There is nothing wrong with solving your problem nummerically!

 

[Jolly Green Tractor]

The primary reason why I was looking for a more elegant solution is that the iterative solution I have created falls apart after only a couple hundred iterations. I have spent several hours looking for the cause of the crash without success.

 

[Jolly Green Tractor]

I am surprised that I cannot find the equations I am looking for online. Does anyone have a suggestion as to where to find a comprehensive ground vehicle acceleration model?

 

[cozyqt]

Soalr Dragster Spreadsheet Calculations

I put together a spreadsheet that includes the effects of acceleration, air drag and rolling resistance. It can be found at:
http://users.applecapital.net/~jim/Dragster_Physics.xls"

There is no guarantee that it is 100% correct. Let me know if you find any mistakes in it because we are building our solar dragster based on these calculations.
When I first ran this, I was surprised to find that air drag was the predominant factor, even though the solar powered dragsters were only reaching a top speed of 30 mph or so. I wonder how many top fuel dragster realize this? They may be able to set new world records if they improve the aerodynamics of their dragsters. The air drag at 200 mph may be considerable, even if you've got 2000 HP to work with.
http://users.applecapital.net/~jim/solardragrace.htm"
Jim White

 

[ray b]

air drag has been greatly reduced over the years
the first ''rail'' cars had all most no bodys or fairing
but also added to
by the large wings used to gain traction

current fuel cars have 6000 hp and go about 330mph
and both are limited by current rules on engine size and gearing

many factors are traded off to get to the current balance
weight traction and drag from wings are some of the major factors
too little wing will limit traction and lose races

 

[cozyqt]

Air Drag Exceeds Acceleration Thrust Above 140 mph

Even with 6000 HP, air drag is an important factor if a dragster wants to reduce their time or increase their top speed in the 1/4 mile.

 

[Mech_Engineer]

...I was surprised to find that air drag was the predominant factor, even though the solar powered dragsters were only reaching a top speed of 30 mph or so. I wonder how many top fuel dragster realize this? They may be able to set new world records if they improve the aerodynamics of their dragsters. The air drag at 200 mph may be considerable, even if you've got 2000 HP to work with.

Even with 6000 HP, air drag is an important factor if a dragster wants to reduce their time or increase their top speed in the 1/4 mile.

Believe me, top fuel drag teams are quite aware of aerodynamic drag; but, they are also aware of many other competing problems, including the fact that it takes a LOT of traction (and therefore a lot of downforce) to put 6000hp to the ground.

Your discovery of air drag problems in drag racing is not particurally ground breaking IMO.