Speed of a car rolling down a hill

[Thecla]

I wanted the hill to be long enough to reach a terminal velocity not at the bottom of a hill. If a 20 mile hill is long enough that will be fine. The car by the way is a normal sedan with standard tires

 

[bob012345]

I wanted the hill to be long enough to reach a terminal velocity not at the bottom of a hill. If a 20 mile hill is long enough that will be fine. The car by the way is a normal sedan with standard tires

Great. That puts it in the range of a real mountain in principle.

 

[Thecla]

By the way would you feel safe in a car free rolling down a 30 degree slope that is 20 miles long? Would you worry the car will fall apart?

 

[jrmichler]

This physics problem can benefit from some real data. A coastdown test on my truck resulted in the drag equation: Drag = 54 lbs + 0.0143 X (ft/sec)^2. The test procedure and calculations are here: https://ecomodder.com/forum/showthread.php/coastdown-test-06-gmc-canyon-20405.html. That coastdown test was done at 17 deg F outside air temperature. The drag would be a lot less at warmer temperatures.

At terminal velocity on a 5% grade, the total drag will be 0.05 X 4650 = 233 lbs. Solving for the velocity at which total drag = 233 lbs, the terminal velocity would be 112 ft/sec = 76 MPH.

Calculating the terminal velocity for a 30 degree slope is left as an exercise for others.

 

[bob012345]

By the way would you feel safe in a car free rolling down a 30 degree slope that is 20 miles long? Would you worry the car will fall apart?

No, I'd worry about me falling apart first.

Also, you asked;

Are there mechanical features of the car that will prevent the car from gaining speed after a certain point?

The engine will act like a brake and limit the speed to some extent if you downshift or with an automatic, shift to Low depending on the circumstances. I could envision a situation where the acceleration due to gravity is matched by the engine braking and rolling friction even without aerodynamic drag for a gentle slope.

 

[berkeman]

By the way would you feel safe in a car free rolling down a 30 degree slope that is 20 miles long? Would you worry the car will fall apart?

As long as you carefully tape the doors shut, you should be fine...

https://arstechnica.com/cars/2020/0...pe-was-rolling-downhill-in-promotional-video/

 

[cmb]

Summary:: Will a car make it to the bottom of a long hill?
... a 5% grade. You start it and put it in neutral or drive and it starts to roll down. You never place your foot on the brake or the accelerator and suppose the hill is 200 miles long.

So, we're talking about a straight grade starting 10 miles high?

Doesn't sound like planet Earth, maybe we need to specify the atmospheric and gravity conditions too?

Nothwithstanding that quip (a pathetic attempt at engineering humour, maybe), but if it really was that long then we're probably talking about different air densities on the descent, so it will surely begin to slow down at the end once into denser air, and pass exactly through a terminal velocity speed at some point.

So need to specify the starting altitude as it would likely reach terminal velocity quicker and earlier. Some of those routes between New Mexico and Colorado might alter the arithmetic!

... 100mph sounds reasonable, considering engineering estimates ...

 

[bob012345]

So, we're talking about a straight grade starting 10 miles high?

Doesn't sound like planet Earth, maybe we need to specify the atmospheric and gravity conditions too?

The hill has been reduced to 20 miles long and 1 mile high in post#31.

As an aside, Olympus Mons on Mars certainly fits the description of the original mountain, complete with virtually no atmosphere to interfere. Perhaps Elon Musk will do this experiment someday with a Tesla on Mars.

 

[Thecla]

I think we are making it more complicted than it needs to be.I will shorten the hill ,but make it steeper . Also ignore different strengths of gravity and different air resisatance. A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?

 

[jack action]

A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?

No, it won't reach 300 mph, because of air resistance. Since we are talking maximum speed of about 100 mph, normal car mechanical components can easily withstand the forces acting at this speed. And since the hill is of indefinite length, it will necessarily reach its terminal velocity before reaching the bottom (since there is none).

 

[bob012345]

I think we are making it more complicted than it needs to be.I will shorten the hill ,but make it steeper . Also ignore different strengths of gravity and different air resisatance. A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?

I do not believe it will reach 300 $mph$. Consider that if the car was dropped from an aircraft it would not reach 300 $mph$ terminal velocity. Here is a terminal velocity calculator to ply with. Given a car in free fall with air drag on the order of 100-130 $mph$ it is only going to be less rolling down a $30°$ hill.

http://www.calctool.org/CALC/eng/aerospace/terminal

You would have a shot at reaching 300 $mph$ on Mars.

 

[cmb]

... Given a car in free fall with air drag on the order of 100-130 $mph$ it is only going to be less rolling down a $30°$ hill.

http://www.calctool.org/CALC/eng/aerospace/terminal

I get 374mph when I do that calculation with that calculator and realistic numbers. What numbers are you using?

 

[bob012345]

I get 374mph when I do that calculation with that calculator and realistic numbers. What numbers are you using?

View attachment 286944

My area was too big by 10x.

 

[cmb]

My area was too big by 10x.

Well, the interesting point there is that it wouldn't be an over-estimate if the car is falling bottom side down, rather than pitched nose forward.

Which raises the next question, if you were to have a car in freefall through air, would aerodynamics pitch it nose first to max terminal velocity, or tumble from one attitude to another, or find the minimum terminal velocity bottom-down?

And then the next question back to the op; if a vertical fall is too steep to stop it tumbling on its way down and a 5% grade isn't, what is the maximum grade before one can expect a car becomes aerodynamically unstable?

 

[bob012345]

Well, the interesting point there is that it wouldn't be an over-estimate if the car is falling bottom side down, rather than pitched nose forward.

Which raises the next question, if you were to have a car in freefall through air, would aerodynamics pitch it nose first to max terminal velocity, or tumble from one attitude to another, or find the minimum terminal velocity bottom-down?

And then the next question back to the op; if a vertical fall is too steep to stop it tumbling on its way down and a 5% grade isn't, what is the maximum grade before one can expect a car becomes aerodynamically unstable?

A car careening down a steep incline should have a lift component as well as a drag component. If the lift becomes significant it will compromise the normal force required to hold the vehicle against the incline and it will fly off into a tumbling catastrophe. One would need the details of a design to figure the lift of a car vs. velocity.