|MadSci Network: Physics|
I have to agree with you on this one, with one reservation I'll get back to in a minute. By the way, I think it's spelled 'Kitt', though I'm not sure. I didn't watch the show much when it was on. ;-)
Say the wheels are spinning such that the car is moving 60 mph. Think of it from the point of view of the car. The road is moving under the car at that speed. Now let the truck ahead of the car slow down a bit so that the car is approaching the ramp (or, from the car's POV, the ramp slowly approaches the car). The wheels of the car touch the ramp. What happens? Well, the wheels are still spinning at a high rate, so the car screeches and zooms up the ramp! Wham! Kitt now needs a repair kit, haha.
Think of it this way: if Kitt were a hockey puck, shooting across the road at 60 mph, then the ramp is moving very slowly relative to it, so slowing down the hockey puck would be easy. But Kitt is not a hockey puck, moving by momentum. Kitt is moved due to the rotation of its wheels. Relative to the road, the piece of tire in contact with the ground is not moving across the road! If it did move relative to the ground, the car would skid. However, that same piece of tire will be moving pretty quickly relative to a ramp moving at the same speed as the car. So Kitt crashes, or at least leaves tremendous skid marks up the ramp.
It would have been better for the ramp to be replaced by a treadmill. The tread could start off spinning at a velocity of 60 mph to match Kitt's ground speed. When Kitt touches the ramp, it immediately starts slowing down. If Kitt brakes correctly, the car can slow down much faster than it could on a static ramp. Better make sure the treadmill is spinning in the correct direction, or else Kitt will accelerate into the truck! Ouch!
My reservation is this: I agree with you that it isn't possible. So how did they film it? I would guess that they did the trick at 20 mph, so the car needed much less space to stop, and then sped up the film. Does this sound right? I think the show is in reruns on cable someplace; I'll check it out and see when I get the chance!
Someone answered this question once already, but they said that it isn't possible for the reason stated in the question (the car will zoom up the ramp at 60mph). Well, your brother and your physics teacher are right…it is possible, but it's not easy. I'll throw in a summary at the end if you want the short answer. Anyway, here's why:
Let's assume the scenario that you stated above. KITT is approaching the trailer at 60 mph and that the trailer is going 1 mph slower (59 mph). As soon as KITT actually reaches the trailer, the tires will be turning at 59 mph relative to the trailer, but the rest of the vehicle will still only be traveling at 1 mph relative to the trailer. The entire vehicle will not instantaneously accelerate to 60 mph on the trailer. And that is the key: the inertia of the vehicle is much greater than the inertia of the drivetrain and tires. In order to be traveling at 60mph on the trailer, the vehicle would have to be traveling 120 mph relative to the ground. This type of acceleration will not happen instantaneously, especially with no outside forces acting on the vehicle (we will assume that Michael Knight aka David Hasselhoff is not going to floor it as he drives onto the trailer).
I worked out all of the physics involved just to prove that this does work. If the physics are over your head, just think of it like this: the car suddenly hitting the ramp with low relative velocity to the ramp, but a high tire speed is analogous to this scenario. Jack up the drive wheels of your car, get the wheels spinning at 60 mph, take your foot off the gas, then drop the car off of the jack. Yes, the vehicle will lurch forward once the spinning wheels hit the ground, but it certainly won't shoot to 60mph, nor will it be hard to slow down.
You'll have to trust me on these numbers as I don't know where you would easily find this type of information. I work for a car company, so I looked up some information on our own cars, and from that picked some values I thought would be fairly reasonable for KITT. Here are my assumptions:
Vehicle weight: 4000 lbs.
- probably about right for that car including driver, and KITT's extra equipment
Drivetrain inertia: .34 ft-lb-sec^2
- trust me. This includes engine, flexplate, torque converter, transmission, and drive shaft
Tire inertia: 1.2 ft-lb-sec^2 / tire
- trust me again. Obviously these numbers aren't exact, but they're in the ball park.
Tire radius: 12" or 1 foot
- probably fairly close, and makes the math easier
Final drive ratio (ratio of the rotational velocities of the tires to the drivetrain): 3.5
- for this car, the drive ratios may have ranged anywhere from the high 2's to the low 4's, so 3.5 sounds good Transmission gear ratio (ratio of the rotational velocity of the engine to the rest of the drive train): 1
- 3rd gear in a 4 gear overdrive automatic transmission. This would be a "worst case" scenario--with the car still in drive, so there is added engine inertia. Although, the car would probably stall, or at least the transmission will be very unhappy when the tires suddenly decelerate from 60 to something much less.
So at 60 mph (88 ft/sec) the tires at turning at 14 revolutions / sec, and the rest of the drive train will be turning at 49 revolutions / second (2940 rpm). Now the total kinetic energy of the car before hitting the ramp can be calculated. This will be the sum of the linear kinetic energy of the entire vehicle (.5 * mass of vehicle * velocity^2) and the rotational kinetic energy of the spinning parts (.5 * rotational inertia * rotational velocity^2). With the numbers given above, relative to the truck, I got 134 lb-ft for the car (1 mph), 408 lb-ft for the drive train, and 470 lb-ft for the tires. Now, if we let the wheels and drivetrain transfer some of their kinetic energy to the car to reach an equilibrium, we end up with a vehicle speed of 4 ft/sec or 2.7 mph. That's all. No worry about that car shooting up the ramp too quickly.
Unfortunately, there are other problems that we must consider if we really want to pull this off. We know that even at 60 mph, the car will not lurch up the ramp at an uncontrollable rate, but there are certainly other vehicle dynamics problems to consider. First, the transmission. Like I said, if you stay in gear, you're very likely to stall the engine, or really make the transmission unhappy. It probably wouldn't stand up to very many of those rapid decelerations. So, you're probably going to have to put it in neutral, then back in gear once you're on the ramp. This would probably be much easier to accomplish in a manual transmission vehicle rather than an automatic.
Next problem is steering. When those 60mph tires hit that 1mph ramp, you can bet that they're going to slip and skid and overall be out of control for a second or two. And when you're front wheels are out of control, that means steering is out of control. At the very least, it's going to be one huge jerk on the steering, and if you want to really pull this off, you're probably going to need to lock the steering straight forward as you approach the ramp just to ensure you don't suddenly get jerked off of the ramp.
Here's another problem that I almost forgot about until talking with a colleague of mine. The suspension. When the tires hit the ramp and suddenly slow down, this will transfer a huge torque to the wheels, which will in turn be transferred to the vehicle, which will make the suspension act. You can think of this almost exactly like the suspension reaction you get from braking. The car lurches forward, right? Well that torque transfer will do the exact same thing, and when the back tires hit the ramp, it will very likely cause the front suspension to drop sharply and probably bottom out. This may cause some serious control problems, if it doesn't suddenly slow you down that last 2.7 mph and drop you back off the ramp. So KITT will probably also need a means to hold the suspension rigid temporarily while driving onto the ramp.
Like I said in the beginning, it may be possible, but it certainly won't be easy. To summarize what will probably happen, the front tires will hit the ramp and cause the car to speed up by about 1mph. This will also cause steering to get a little rough for a moment while the tires come to equilibrium with the ramp. When the rear tires hit, the car will again speed up by about 1 mph. If you're still in gear, the engine will probably stall. The force of the tires slowing down rapidly will also cause the front of the vehicle to dip sharply and probably hit the ramp. It's not going to be pretty, but it can be done if you plan ahead and properly prepare the vehicle. In other words, don't try this at home.
Mike "Chuck" Scannell
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