Car down boat ramp into water 120', how fast?

November 1, 2005 7:12 AM

A car travels down a boat ramp into the water then travels 120 feet out into the lake. How fast was it going when it hit the water?
posted by Floydd to Science & Nature (34 answers total)

Depends on the size / weight / cross section / buoyancy of the car, its surface friction, the viscosity of the water, whether or not it hits the bottom of the lake, how still the water is...
posted by signal at 7:18 AM on November 1, 2005

Also length and angle of the ramp, whether there is any tide in the lake, wind, any number of variables.
posted by spicynuts at 7:28 AM on November 1, 2005

Seventy-four miles per hour, under certain conditions.
posted by Plutor at 7:39 AM on November 1, 2005

Yea... I agree, not enough information to say for sure. But my GUESS would be "reasonably fast"? Under 50 but above 30?
posted by Witty at 7:40 AM on November 1, 2005

Pretty fast by my initial reckoning and plodding arithmetic. If you assume the car flies through the air taking a second to travel the 120 feet before crashing into the water then it would have travelled 120*60*60 feet in an hour. Divide by 5280 to get miles gives 81.8 mph. The water is about 1,000 times more dense than the air so I'd guess most of the journey from the end of the ramp would have had to be airborne.
posted by rongorongo at 7:43 AM on November 1, 2005

Why would the length of the ramp affect anything?
posted by delmoi at 7:43 AM on November 1, 2005

Under 50 but above 30?

Really? My guess would be that depending on the angle of the ramp, the design of the car (in particular how large and what the angle of the front grill is), how far forward the engine is and how heavy it is, how much air the passenger compartment holds and for that matter whether the windows are shut or not, the car could pretty much do ANYTHING. Options include:

a) slam grill first into the water and immediately stop then sink;

b) slice into the water at an angle and use most of its energy to travel deeper into the water rather than farther out, then sink;

c) catch the water with the front tires at a strange angle causing the car to spin in the water thus using most of its energy to turn rather than go far out.

I guess my point is that this is an impossible scenario to predict.
posted by spicynuts at 7:47 AM on November 1, 2005

rongorongo: The question asked about a car going down a boat ramp, not up it. i.e. there is no air travel involved.

I just don't think it would be possible to answer this question. The over-riding force acting on the car would be the viscosity of the water, which in turn would be greatly affected by the shape of the car.

Also, if the car could float for a couple of minutes before sinking (like if the doors are closed) it may be that the car was only crawling along when it hit the water, and floated the rest of the way, carried by currents.
posted by delmoi at 7:47 AM on November 1, 2005

Why would the length of the ramp affect anything?

Because it was not declared whether this car is driven at a constant speed or simply hits the ramp at a given speed and thus is slowed down over the course of traversing the ramp due to friction and resistance from both the ramp and the air.
posted by spicynuts at 7:48 AM on November 1, 2005

120 feet out? did this really happen? from the description i can't see how it flew (boat ramps slope down - you don't launch your dinghy into the air!). so i'm guessing either the water isn't very deep, so it drove for much of that distance, or it skated across the surface. and it's difficult to say much about skating across the surface because there's nothing simple to get a physical handle on (pushing through water you can calculate masses pushed aside etc, but skimming over the top isn't like that).
posted by andrew cooke at 7:50 AM on November 1, 2005

A boat ramp goes down into the water, so a car traveling down the ramp is not going to fly off the ramp, it's going to hit the water. But then it might bounce once or twice like a skipping stone, but would have to be going damn fast to do that. Rongorongo's calculation is probably not far off, but there is no way to calculate it exactly.
posted by beagle at 7:50 AM on November 1, 2005

You need the angle of the ramp.

I can tell you, however, that the 120 feet into the water is meaningless. It can't help you without knowing all sorts of things about the car and about water.

All you need to know is the height or angle of the ramp (you can get the other one if you have one of these two). Knowing the coefficient of friction on the axles of the car would be helpful too, but can probably be left out as the difference won't be monstrous.

I've been out of physics too long though, so... I couldn't tell ya the formula now... d'oh.
posted by twiggy at 7:51 AM on November 1, 2005

Er, I don't mean that the actual viscosity of the water would be effected by the shape of the car (viscosity is basically a constant, when you're not counting temprature/pressure/impurety/etc) but how the water flows around the car would be affected primarily by the shape of the car.

I guess my point is that this is an impossible scenario to predict.

Pretty much, yeah. It could do anything. If you had a super computer, you could maybe figure something out. Fluid dynamics is one of the most common application for super-computers.
posted by delmoi at 7:51 AM on November 1, 2005

The car enters the water. At that point, there are three options:

1) It floats. If it floats, almost any amount of speed is enough to get it to 120 feet out. It'll just take a while.
2) It sinks, and travels underwater on the concrete ramp all the way to 120 feet. This is an unusual ramp. This would require considerable initial speed.
3) It sinks, and goes to the end of the ramp, and then gets stuck in the mud. No way it's going 120 feet. No speed would overcome the resistance.

So my answers are 5 mph, 100 mph, and not answerable.
posted by smackfu at 7:51 AM on November 1, 2005

Are we talking about this car found 120 feet from a boat ramp? (Google cache; site requires registration)
posted by beagle at 7:54 AM on November 1, 2005

< 11.2 km/s
posted by gi_wrighty at 7:55 AM on November 1, 2005

smackfu: It could also skip like a stone, but this seems pretty unlikely, and impossible to predict. (and it would need to be going really fast).

But the most likely answer is that it just floated out that far, in which case it doesn't matter how fast it was going.
posted by delmoi at 7:55 AM on November 1, 2005

This was an issue in the Susan Smith murder trial. She just let off the brake while parked on the boat ramp and let her Mazda Protege kind of...float into the lake, her two sons inside. If I recall correctly, investigators didn't find her car at first because the car, under a slow roll, went much further out into the lake than they expected it would. A chilling, chilling case.
posted by GaelFC at 8:03 AM on November 1, 2005

If the floor of the lake is sloped down, it need hardly be moving at all. It would just roll slowly until it came to rest a local minimum.
posted by gleuschk at 8:05 AM on November 1, 2005

Is the lake frozen?
posted by Pollomacho at 8:17 AM on November 1, 2005

Response by poster: Wow. I leave for a few minutes to do some "work" and look at all the responses!!
This really happened last weekend. (Scroll down)
It sounds like the car hit some rocks before it went in the water, but it happened in broad daylight and only one of the bodies has been recovered, leading me to believe that the car must have been travelling at a high rate of speed when it went in, since the occupants were seemingly rendered unconscious by the impact.
posted by Floydd at 8:27 AM on November 1, 2005

Well, it is possible for a non-floating object to skid on water, given enough speed. You would have to figure how much speed is required for that car with those tires to skid on water, figure out how fast it slows down and then figure out how much speed it was going on when it hit the water. Not an easy task. They did a stunt like this on the UK motoring show Top Gear, it was done with a icelandic 4x4 racing buggy and wide tires, but it was driven on water for hundreds of meters. I'd say the speed required for the car to do it would be considerable and it doesn't seem like this happened in this case.
posted by lazy-ville at 8:28 AM on November 1, 2005

Seems to me the most likely situation is that the car takes a while to sink. There's air trapped inside, which slowly leaks out, so at first it kinda floats a bit, then it sinks. How far out it goes before it hits the bottom, if the lake is of any significant depth, then depends largely on what angle it's at while it sinks.

Assuming the engine is in the front, it's going to move forward while it sinks.
posted by sfenders at 9:22 AM on November 1, 2005

it is possible for a non-floating object to skid on water, given enough speed.

For snowmobiles, that isn't all that much speed, and they're probably much less buoyant than a car. But they are also a better shape for that, and without propulsion, they'll stop and sink pretty fast, like within ten yards or so I'd guess, even when you're going fast.
posted by sfenders at 9:27 AM on November 1, 2005

there's another factor at work here ... this is lake michigan, so the undertow could have taken it a bit further out than it landed
posted by pyramid termite at 9:32 AM on November 1, 2005

Response by poster: I think I asked a question that can't be answered given the information we have.
What we know is the boat ramp slopes down to the water.
The car had two occupants.
The road they were on ends at the water, it's a straight shot for 100 yards or so to the water.
It was daylight, dry pavement, good visibility.
The car ended up 120 feet from the end of the pavement.
One occupant is dead, the other presumed dead.
That's all I've got, and, given the fact that some of the best minds I know have (anchors a-)weighed in on this, I don't think this one can be answered with the information at hand.

(go ahead, prove me wrong!)
posted by Floydd at 9:48 AM on November 1, 2005

The problem with answering it is that there is no way to be certain that the 120 feet is due to floating out there after going into the water and stopping or the end point of the car's kinetic energy.
posted by spicynuts at 10:02 AM on November 1, 2005

Uh, the best way to find out would be to buy a couple vehicles like that and do some experimenting.
posted by delmoi at 10:07 AM on November 1, 2005

I don't know if it was the Susan Smith case or an episode of CSI... but it depends alot on the air-tightness of the car. A more air-tight will float longer and be carried farther by a current. A non air-tight car (lots of cracks, windows open) will fill up quickly and sink like a stone.
posted by clh at 10:07 AM on November 1, 2005

sfenders writes "For snowmobiles, that isn't all that much speed, and they're probably much less buoyant than a car."

We used to race snowmobiles across the Thompson River in BC,





in the summer when there was no ice.
posted by Mitheral at 11:48 AM on November 1, 2005

The impact doesn't have to be forceful for you to die in a submerged car. It is a difficult situation to get out of, even if you know the proper steps to take (open the windows, let the water come in the car, then swim out through the window). You won't be able to open the door against the pressure of the water.

I'm going with the "car floated away" story, rather than the car was going so fast that it went 120 feet out into water (nearly impossible).
posted by knave at 11:59 AM on November 1, 2005

I agree with knave. My first calculation ignored the ramp and assumed a horizontal pier with a "flight time" of 1 second before hitting the water (and sinking vertically to its final resting place). However the pier would have to be about 30 feet high to allow for that 1 second drop to the water 120 feet out. At 80mph.

So given a ramp that goes right into the water I don't think there is any feasible initial velocity achievable by a car that could have got 120 feet out straight away. Therefore the car MUST have floated out for some of the distance (and I think only forensic evidence such as tyre marks on the ramp or impact damage on the car could give an idea of how fast it was going).
posted by rongorongo at 2:05 PM on November 1, 2005

The problem with the "car floated away" theory is that this is Lake Michigan. Any current (i.e., wave action) would be directed towards the shore, wouldn't it? Until the car got some distance out, wouldn't the waves tend to carry it back towards shore?

The distance/velocity/time question is a matter of deceleration -- what are the forces acting on the car to oppose its initial velocity. In this case, there are two separate decelerations: the first is at the boundary where the car first hits the water; this is a sudden spike of deceleration. The two main contributing components to this deceleration are the cross-section of the car and the fact that water is not easily compressed, so the car would have to move a column of water out of the way (think about belly-flopping into a pool). This initial deceleration would rob the car of a lot of momentum and would probably provide much of the damage to the occupants.

Since the car did not hit perpendicular to the plane of the water, however, it would still retain some forward velocity. The second deceleration occurs as a function of the drag coefficient (viscosity, cross-section, etc.) and is a simple equation: distance = velocity x time - 1/2 x deceleration x time ^ 2. If you knew the drag coefficient, you could determine the deceleration. However, you have two unknowns (time and velocity), so you can't solve the equation. That's moot for your original question, anyway, since it would only provide a solution for the second stage of deceleration and not allow for the first stage. And now I'm going back to pondering my navel.
posted by forrest at 5:00 PM on November 1, 2005

... actually there might be more like four or five distinct phases: make a splash (or very briefly plane), slow down to "hull speed", slow down below hull speed while still floating, then accelerate forward while sinking. The great majority of the distance covered would be in the last two. How much in each would depend on how deep the lake is, and how fast the car fills with water.

It would very quickly slow down to "hull speed" which I guess is probably less than 5 mph for a floating car. I bet a car going 60mph would end up on average less than 20 feet further out than a car going 10mph.
posted by sfenders at 6:04 PM on November 1, 2005