what will the speed be of a car driving at say 20mph onto the back of a truck driving at 10mph.(as seen on tv programs such as Fear Factor and the OLD Knight rider)
Either at the time the car reaches the ramp onto the truck or on the back of the truck.
There has been lots of deliberation around this point.
Thanks for a great site.
Yabbie
South africa
The way you pose the problem, it sounds like you’re thinking about two scenarios: either the car speeds up to 30 mph (relative to the road) and the tires maintain rolling contact on the ramp, or the car remains at 20 mph (again, relative to the road) and the tires slip or slow down after they touch the ramp.
The inertia of the car is far too high – relative to the inertia of the tires and the frictional force needed to make them slip – to cause it to instantly accelerate once the wheels hit the ramp. Thus, the tires slip briefly, and the car keeps moving up the ramp at about 20 mph (relative to the road), or 10 mph relative to the ramp.
Another way to think about this is to start with the car on a moving ramp (say, 60 mph), and slowly (1-2 mph) roll it backwards onto the road. As soon as the wheels touch the pavement, they will slip and very quickly spin up to 58-59 mph as the car keeps moving forward – it’s very similar to what happens to an airplane’s landing gear as it touches down.
On preview I agree with KeithT but will post my little thought experiment anyway.
I hope nobody mentions the airplane and conveyer belt.
I do not have a factual answer in terms of having seen this done, and I haven’t seen it on TV except for a car commercial where it may have been special effects rather than real.
Assume you have a car driving 20 MPH approaching a truck going 10 MPH with a ramp dragging behind it. Assume the car is front-wheel drive. When the car’s front wheels hit the ramp, if they maintained the same speed then the car would drive up the ramp at 20 MPH relative to the truck. This is probably a bit fast for climbing a ramp onto a truck. However, the car is probably not going to maintain 20 MPH relative to the ramp for two reasons.
The car hitting the truck ramp is not a free ride for the car. Although the truck is pulling it at an added 10 MPH, the car has to hold on and pull itself along with the truck to overcome its inertia.
Let’s assume away a couple of things to simplify the model. Assume that the truck is a moving flat surface flush with the road, as though it were a moving piece of road. If you have ever been on an airport “people mover” you are very familiar with this idea. Think of the sensation you have when you first step onto the people mover. Although it is moving, it is not a totally free ride. When you first step on it, you have to push a little harder for a second if you want to keep walking. (Same thing in reverse when you step off; you have to decelerate.) When the car hits the truck ramp, the truck’s speed, faster than the road, requires the car to temporarily increase power to maintain 20 MPH relative to the truck (which is 30 MPH relative to the road). This assumes that the tires won’t slip under the extra power. Without the extra power surge, the car will not be able to “hold on” to the truck enough to maintain 20 MPH w.r.t. the truck, and the car will reduce its speed relative to the truck, as if it were going up a hill. However, it will still roll forward due to the fact that it was going 10 MPH faster than the truck. (If the car shifted into neutral when it hits the truck, then it would simply roll forward at 10 MPH w.r.t. to the truck, maintaining its original 20 MPH w.r.t. to the road.)
When you add the ramp back into the equation, the car has to climb uphill on the ramp, and that climb starts rather suddenly, unlike usual road conditions. The car would have to increase power instantaneously to maintain speed.
So the answer is 10 MPH or greater w.r.t. the truck depending on how much gas the driver gives it when reaching the ramp. If the driver applies brakes after reaching the ramp (probably a good idea unless he wants to drive right over the truck) then it will be less.
So the real answer is, “Any speed. It just depends.”
Heh. I almost used the analogy of landing on a treadmill, but my better judgment took over. 
I was going to say that the last time this came up, the results were about as bad as the treadmill thread.
What about rear wheel drive versus front wheel drive cars? Would FWD work?
Sure, anything would work. The momentum of the car is most of what carries it up the ramp, not the drive wheels. If you match the speeds very closely then the drive wheels will come into play more. But front or rear would work pretty well either way, as long as there’s enough weight over them to get traction.
It would be interesting with modern skid control would the computer would think of the front wheels rolling at 10 MPH and the back wheels at 20 MPH. It might decide to apply brakes in the middle of the transfer, and wouldn’t that be fun?
Speaking of those people movers at the airport, has anyone ever tried riding a bike onto one of those? Or any other type of self-propelled vehicle? It seems like it’d be a similar scenario.
You would or should put the clutch in as the drive wheels hit. They will be going from 20 mph to 10 mph near-instantaneously, which would put a strain on the gearbox and engine. The clutch need only be in for that instant, then you’d let it out again to power up the ramp. This might be a little easier to time in a front wheel drive.
? WHAT ?
You just did!
Now to muddy the water just a bit. Does the car have a front or rear wheel drive? Does it make a difference?
It is the relative speed of the car to the truck that is the matter to be considered.
Consider the truck stationary and the car moving at 10 mph.
When the driving wheels of the car access the truck bed/ramp/or? the driver had best hit the brakes when all 4 wheels are on board and FAST. (Unless it is a long bed trailer.)