Almost nowhere is my assumption. Might roll slightly forward if we assume the wheels and axles survive being dropped.
So let’s do some shoddy calculations.
The amount of kinetic energy in a spinning wheel can be described as
KR = 1/2 × I × w^2
Where KR is rotational kinetic energy
I is rotational inertia
And w is angular velocity
Assuming the wheels are uniform cylinders their rotational inertia follows
I = 1/2mr^2
Where m is mass and r is radius
Let’s take a car, say the Toyota 86. It’s wheel radius is about 0.2m and it’s wheel weight is about 10 kg so it’s rotational inertia is about 0.2kgm^2
Therefore it’s KR at 100mph (45ish meters per second) is
1/2 × 0.2 × 45^2 = 202.5J
Multiply by the 4 wheels we get about 800J of rotational energy
Lets assume all of this rotational energy gets turned into kinetic energy punching the car forward. (This is beyond generous)
To find it’s velocity forward we can use
KE = 1/2mv^2
Where KE is kinetic energy
m is the mass of the car (about 1200kg for a Toyota 86)
And v is the velocity
Rearranging 800 = 1/2 × 1200 × v^2
Gives v to be 1.15m/s
Or about 2.6mph
You can sort of intuite how far a car will roll forward when it’s at 2.6mph and you’re not giving it any more gas, if not the answer is not very far, I’d guess maybe a meter or so. It should be noted that this is a gross oversimplification that glosses over details that would make the car move LESS far. Cars are driven forward by the power being applied constantly by the engine and not by the momentum in the rotating tyres. I’d love to hear others thoughts on this problem and if you agree or disagree with my methodology :)
I agree with your methodology and I’m further stoked to see that my assessment, which was largely a guess generated by inverting the relative speeds and masses of the body of the car and its wheels, arrived at a rather similar result. Neat.
(I used the weights from my Crosstrek, which is a bit heaver than a GT86 and mine at least has larger diameter wheels, but coincidentally uses an engine based around the same design. FA/FB gang, yo.)
Almost nowhere is my assumption. Might roll slightly forward if we assume the wheels and axles survive being dropped.
So let’s do some shoddy calculations.
The amount of kinetic energy in a spinning wheel can be described as
KR = 1/2 × I × w^2
Where KR is rotational kinetic energy
I is rotational inertia
And w is angular velocity
Assuming the wheels are uniform cylinders their rotational inertia follows
I = 1/2mr^2
Where m is mass and r is radius
Let’s take a car, say the Toyota 86. It’s wheel radius is about 0.2m and it’s wheel weight is about 10 kg so it’s rotational inertia is about 0.2kgm^2
Therefore it’s KR at 100mph (45ish meters per second) is
1/2 × 0.2 × 45^2 = 202.5J
Multiply by the 4 wheels we get about 800J of rotational energy
Lets assume all of this rotational energy gets turned into kinetic energy punching the car forward. (This is beyond generous)
To find it’s velocity forward we can use
KE = 1/2mv^2
Where KE is kinetic energy
m is the mass of the car (about 1200kg for a Toyota 86)
And v is the velocity
Rearranging 800 = 1/2 × 1200 × v^2
Gives v to be 1.15m/s
Or about 2.6mph
You can sort of intuite how far a car will roll forward when it’s at 2.6mph and you’re not giving it any more gas, if not the answer is not very far, I’d guess maybe a meter or so. It should be noted that this is a gross oversimplification that glosses over details that would make the car move LESS far. Cars are driven forward by the power being applied constantly by the engine and not by the momentum in the rotating tyres. I’d love to hear others thoughts on this problem and if you agree or disagree with my methodology :)
I agree with your methodology and I’m further stoked to see that my assessment, which was largely a guess generated by inverting the relative speeds and masses of the body of the car and its wheels, arrived at a rather similar result. Neat.
(I used the weights from my Crosstrek, which is a bit heaver than a GT86 and mine at least has larger diameter wheels, but coincidentally uses an engine based around the same design. FA/FB gang, yo.)