What incline is needed for various vehicles to coast at a given rate?

Question

I have been studying sailplanes, and efficient movement. Now I was wondering how efficient land vehicles can move as compared to sailplanes. An efficient sailplane can glide at 60 mph on a slight 60 to 1 incline, which slight incline a bicycle likely could hardly coast on. That slight incline gives the glider thrust to both overcome head on air resistance and thrust to attain it's lift in mid air.

If any one can help with any of the below questions it would be much appreciated.

I was wondering how much incline or slope a loaded train with many cars would need to coast along at 60 mph. A train would likely need the least slope as it would have very little air resistance and has wheels that cause very little friction.

How much slope would a load semi need to coast at 60 mph?

How much slope would a typical car need to coast at 60 mph?

How much slope does the most efficient wheeled machine need to coast even at a slow rate?

Answer 1

I do not know the answer (yet). However, I suspect that you would be surprised how much friction there can be in a rail-car wheel. And there are 8 of them per rail car (lots more on the locomotive).

In a "hump yard" they release loaded rail cars down a slope. Depending on the load of the car, the state of the wheels and the wind, etc., each rail car reaches a different speed by the time it reaches the bottom of the slope.

Computers detect the speed of each railcar and, in order to ensure a smoth coupling when the car is sent to the proper track, the computer runs a "retard": a braking system that slows each car to a common, standardised speed.

Every once in a while, usually a lightly loaded railcar with lots of friction in the wheels, the car arrives at the bottom with insufficient speed (the computer cannot accelerate slow cars) and it fails to couple with the other rail cars.

All that to say that it will be difficult to estimate a slope without specifying what friction factor you want to use. In reality, there is a very large variance from rail car to rail car.

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PS:

Galileo's experiments with gravity was done using inclines. What he showed is; if you ignore friction, then objects going down a slope keep accelerating; they do not "coast".

They will coast when the force they get from the slope is equal to the force engendered by friction(s). Once the net force is zero, then the object "coasts".

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PS(2): One hump yard (Haggesville) has a grade of 1.08%. Rail cars with little friction could reach up to 10 or 12 mph in most yards, but the retarder will slow them down to a more decent 8 or 6 depending on the type and content (as low as 4 mph for some kinds of hazardous materials).

Answer 2

I don't have specifics, so I'm anxious to see if someone else does. Sounds like the start of a good science fair project.

A sailplane is extremely clean aerodynamically. It doesn't need much lift to stay aloft. With updrafts, it can stay aloft indefinitely.

A train with its engine disengaged (rare) has extremely low air resistance and rolling resistance. The challenge for any train on a downhill slope is preventing excessive speed increase. It takes a long time to stop a train even if you apply the brakes on all wheels and stop them from turning.

The only coaster I can think of that even approaches the train is a spacecraft. It could coast practically forever. The loaded tractor/semi-trailer is close, but it has higher air resistance and much higher rolling resistance. With engine braking, it can handle downgrades much steeper than any train.

Answer 3

the slope in the distance-time graph is the speed of the object. the steeper the slope the faster is the rate of motion. the bigger the inclination the greater is the speed.