brushman

Current discussion with a friend:

Car A has more 287 hp / 274 torque and more weight (3188 (lbs)
Car B has less 240 hp / 153 torque and less weight (2810 lbs)

Car B and Car A are equal in a straight line acceleration

Going up a 35 degree incline will Car A or Car B win in a straight line race?

Assumptions: (gears are equal, and drivers are equal)

Please show math.

PLEASE DO NOT ARGUE which is better HP or TQ.

The reason for the discussion is: will the more "torquie" and heavier car have and easier time accelerating up the hill than the less "torquie" and lighter car.

THANKS

JL9000

Are you planning on racing a 350Z on a 35 degree incline?

brushman

[QUOTE]Originally posted by JL9000

ellisnc

this problem cannot be done with out torque curves and gear ratios...

Zoran

Since their forward acceleration is the same, we have:

f1/m1 = a1 = a2 = f2/m2

where f, a and m are the two forward thrust forces, accelerations and masses of the two cars.

f1, m1, f2 and m2 are the same regardless of whether the cars are going uphill or downhill.

On an uphill race, the forward thurst the cars generate is the same, but are now reduced by the gravitational force:

F1 = f1 - g*sin(L)*m1

F2 = f2 - g*sin(L)*m2

where L is the angle of the uphill, and g is the gravitational acceleration constant (9.81 m/s^2)

The resulting accelerations will be:

A1 = F1/m1 = f1/m1 - g*sin(L)
A2 = F2/m2 = f2/m2 - g*sin(L) = f1/m1 - g*sin(L) = A1


So if the cars were dead even on the flat ground, they will still be dead even in an uphill race.

brushman

Does the extra weight of the heavier car increase the force needed to go up the incline, thus making it slower?

Zoran

As you can see from my post above, it can perfectly well be done without any specifics of the two cars.

If the two cars are even on flat ground, they will be even on an uphill and on downhill.

If they are not even, the absolute acceleration difference will be the same regardless of the slope.

So if the car A "walks" car B on the flat ground, it will "walk" the car B on an uphill as well, at EXACTLY the same rate it was doing it on the flat ground.

This, of course, is if we ignore the drag effect. If the drag coefficients are drastically different for the two cars, then going downhill the car with less drag will have an advantage, while going uphill the car with more drag will have the advantage, assuming they were even on the flat ground.

Zoran

[QUOTE]Originally posted by brushman

JL9000

The problem can be solved without knowing hp or torque of the cars.

As my prof used to say, "If you can't think any harder, think differently."

Penforhire

Zoran has it right. Nicely put Zoran. If acceleration is the same on the flat then you have the mathematical relationship he (or was it Newton?) described, ignoring lower-order effects like wind resistance, rolling resistance, ...

At some slope, in reality, Car "x" may accelerate better than Car "y" because of traction or some other effect, but not due to the weight/engine difference.