# Why a Car on Skis Only Jumps So Far

The BBC’s clever automotive show Top Gear recently staged its own vehicular version of the Winter Olympics. The high point—pardon the pun—was when they launched a rocket-powered Mini off a ski jump. Despite the extra kick provided by the rockets, the Mini failed to match the distance of a real Olympic ski jumper. Why?

Once an object leaves the ground, we can forget about everything but four simple forces: (1) lift, which opposes (2) gravity, and (3) thrust, which opposes (4) drag. In an airplane, the engines produce enough thrust to overcome the drag created by the airframe punching a hole in the sky at hundreds of miles per hour, while the wings create enough lift to fight gravity and keep the plane aloft.

Our example is a bit simpler. A ski jumper lacks thrust, and, as we see in the video, even the Mini’s rockets are largely exhausted by the time it runs out of ramp. So we can ignore that component. Drag is important, but uninteresting, and ultimately less critical than the other two forces: lift and gravity.

Ask 100 scientists and engineers what causes lift, and most of them will probably give you some version of the nonsense the rest of us learned in school: high pressure below a wing, low pressure above. Wrong! This is a typical consequence of lift, but it’s not the cause. What creates lift, as deftly explained here by the folks who put the first “A” in NASA, is what they call “turning” the air. As air passes beneath a wing, the wing pushes that air down. By Newton’s third law (the one about every action having an equal and opposite reaction), the air must also push back up on the wing. This push is lift.

What does all this have to do with our Mini? Well, a stocky car on skis isn’t pushing air in any one direction, it’s just pushing it out of the way. That means it isn’t producing any lift. A ski jumper, on the other hand, positions her body and skis in a very precise way so as to maximize a net downward push of air. She pushes down so that the air might push back up.

But we must subtract from this push the persistent force of gravity. Fair enough. Fortunately for our jumper, the force of gravity is proportional to an object’s mass, and so the Earth pulls her down with a force less than a tenth the magnitude of the Mini’s. So our jumper’s net acceleration will be her lift (which is small but important) minus her gravity, while the Mini’s net acceleration will be its lift (which is zero) minus its gravity (which is an order of magnitude higher than the jumpers). Result: Even though the Mini might take off at a higher speed, it drops so much faster than the skier that their jump distances can’t compare. —Michael Moyer

Lift is generated by turning the air. However, the following sentence in your post about Newton’s third law isn't quite right, as is explained here: http://www.grc.nasa.gov/WWW/K-12/airplane/wrong2.html

Yes, the force of gravity on the Mini is much higher than the force on the skier, but the Mini's inertia is also much higher. The net acceleration of each object is not the lift minus the force of gravity, but (lift - force of gravity)/mass.

Right - acceleration due to gravity is constant for all objects in free-fall, so what you said about gravity having different magnitudes makes no difference on the Mini. So the only thing in your explanation that is valid is about lift, which is also not completely accurate.
In my understanding, the upward force on a ski jumper is not only from lift created by his forward movement. Instead it is caused by the upward drag on the skiier's body as he falls he positions his body so that his upwards drag is at maximum and his backwards drag is at a minimum, thus allowing him to keep moving forwards and slowing his fall at the same time.

What might make a bigger difference is that the backwards drag on the mini will be huge compared to that of the skiier.

I knew there would be someone who would mistake the acceleration of gravity for the force of gravity.

The force of gravity is indeed proportional to an objects mass, but I do think the argument for lift having anything to do with these jumps is a little off. Isn't the force that is acting against gravity friction? Those big wide ski's are a large area to punch through the air compared to the skiers weight. The skier is more falling slower, which results in a farther jump. The same reasons a feather falls slow and a parachute works.

Air turning is what causes lift, and I am glad to see PopSci setting the record straight on the myth we were all taught in grade school. However, I opened my daughters science book just this year and found this crap is still being taught to children. Well, I guess it is better then Intellegent Design. (whew! Dodged a bullet there.)

The Mini could have gone further, albeit through thrust alone. I was involved in undertaking the calculations for the Rocketmen (Colin Rowe and Damian Hall) who built the Mini. It was decided before the firing, that 3 hybrid rockets would be used instead of 4, since there was some concern that the Mini would flip because of the increased speed off the ramp inducing a noseup attitude. This was also a concern with 3 rockets, although the actual firing indicated that 4 rockets could have been used without the Mini flipping over, and the Mini would have gone quite a bit further.

This is the most incorrect analysis that I have ever seen on what makes an airplane fly. It is a disgrace for Popular Science to give this author a forum for such unscientific notions and opinions. Your magazine has degraded and confused the science of flight. The editoral staff should be ashamed. I am a mechanical engineer and a retired commercial airline captain with over 20,000 hours of "flying" experience.

The PopSci explanation that the wing pushes the air down so the air pushes the wing up works for the skier or a plane climbing or diving, but not for a plane in level flight. . The ski jumper adjusts their angle of attack to optimize maximizing lift with minimizing drag. Elevators on the tail of a plane adjust the entire plane's angle of attack so it climbs or dives. Like the skier, the air is pushed down and the object up. For level flight of a plane, the classic flat-bottom curved-top shape of the wing creates lower air pressure above than below, to compensate for gravity. Don't throw out that grade school textbook just yet. And the skier goes farther, because their ratio of mass to the surface area creating lift is lower than the car's. This is also why cows don't fly. And I have zero air miles as a pilot -- so big rasberry to y'all.

One thing I think everyone is missing... is there any additional spoilers to crerate downforce? the rocket alone are positioned in a way to create downforce wich becomes irrelevent by the jump... However there is still downforce created from the windshield and shape of the car. at 60 mph there may not be any but at 200+ mph there is downforce, and from the looks of how controled the jump was downfoce played a major role in this film.... If there wasn't downforce present during the jump the car would most likely flip up when it became airborn....

I cant make out what is on top of the car, its awfuly big to be a camera. it almost looked like rockets pointing the oposite direction.... closer review of the movie I see that the front of the car hits the ground first and if there was more hang time it would have caused the car to Endo...But regardless of how planes fly the authors point was the aerodynamics is what caused it to go short/ long.... If you turneds the car upsidedown and put ski's and rockets on it you praobably would have seen an slightly oposite reaction...

Hello all,

I hope nobody objects if I chip in a little. Even if perhaps some of the chirping is slightly off topic. :)

My company designed and executed this project for Top Gear in partnership with "Bicker's Action Ltd". Michael Moyer is 100% correct in his analysis.

The project was the subject of a detailed simulation and modelling exercise (like many of our projects). The mini actually landed within 5 metres of where we predicted. From the off, it was made clear to all concerned that the mini would never beat the ski jumper on the basis that the mini was unable to generate lift once it departed from the ski jump. Michael is spot on.

During the initial costing and scoping exercise we briefly examined the possibility of upping the installed rocket thrust to have a departure speed, from the jump, of around 250mph. This was quickly ruled out on the basis of safety. The drawback was the uncertainty that the mini would stay in its tracks during the boost phase down the ramp. Hence for safety reasons we opted for a maximum departure speed of no more than 90 mph.

Bob Mc and Levi B discuss the use of active or passive aerodynamics, none were used; passive lift generating devices would have introduced an unwelcome effect during the vehicles descent down the jump where it was important that the mini stayed firmly in the slots that were cut for it. Lift generating devices would also have detracted from the ‘look’ of the mini.

Also worth pointing out is the main factor involved in the mini pitching nose down after it left the ramp… The primary mechanism here involves a turning moment generated by the front end leaving the ramp first, whilst the back end is still supported. At the speeds involved any aerodynamics thereafter would, I believe, be second order.

With respect to the “items sitting atop the car” What you actually see popping out the top of the mini were the oxidiser tanks for the rocket motors. I can’t, off hand, think of any other application that utilises rocket motors for propelling something downhill. Hence we had to modify the rocket motors (they utilise a liquid oxidiser and solid fuel) to ensure a positive liquid feed to the combustion chamber; that’s why they emerge through the top of the roof like that. The same tanks required filling (fuelling, if you like) just prior to launch. The plumes of white gasses emerging from the vents sited atop the rear of the vehicle indicate to us that we have a full load of liquid oxidiser on board. Thereafter we are in a position to remotely disconnect the fill umbilical and prepare for launch.

We do use lift generating devices in our next project…. “The Robin Reliant Space Shuttle”. Take the Space Shuttle complete with external tank, SRBs and Orbiter and replace the Orbiter with a winged and finned Reliant Robin… you’ll have to tune into Top Gear in February/March to get a look at that and see what happens; I’m not saying anything else. 

Happy landings

Damian Hall
MD The RocketMen Ltd.

P.s. As an aside, regarding the comments above, by ‘Richard Osborne’: He took no active part in the modelling and simulation of the mini ski jump project. The reasons and conclusions made in that post regarding the number of motors used and it’s relation to the mini flipping are also incorrect. Why someone would want to post in this respect: I don’t know.

Hey Damian,

I have a question about Jeremy Clarkson. Did he do anything during that segment other than serve you guys Earl Grey?

Also, how many times did James May slide down the slope and why can't I stop laughing?

Zumba

If popular science REALLY thinks that this is how lift is generated, then they must agree with Newton that flight is impossible (one of Newton's few mistakes, but its true, he said flight was impossible b/c he only considered the momentum effects and not the pressure effects). Boeing and the Wright Bro's might have something to say to you about that though. . .

In the case of a ski jumper, pressure differential doesn't create lift, they are right, b/c there is nothing to generate a pressure differential, a ski is just a plank, not an airfoil, so this is the only sort of lift it can generate.

However, for airplanes in level flight, it is not the momentum effects, or turning effect, that generates lift, or at least these momentum effects only account for a VERY small % of the lift force. It IS the pressure differential, PERIOD. I agree with a previous poster that this site should be disgraced at such a TERRIBLE explaination of how lift works.

The reason NASA talks about turning effects on their site is b/c the momentum effects do dominate lift calculations in rarified air (air that is significantly below atmospheric pressure) or at hypersonic Mach numbers (M>2.5), but again, a very rare case, and to think that this applies to your silly Mini on skis is misleading at best, downright irresponsible at worst.

wtf a bunch of science nerds figuring out why a mini wouldn't go farther then a skier, who gives a fu**

Oh come on you geeks!! They hooked a bunch of rockets on a car and sent it flying off a ski jump, and all you nerds can talk about is Newton's law and mass vs gravity!!! Come on now, it's ROCKETS!! Destruction!! Get a life!!

Great post but Chris does have a good point there lol :)

Dennis

Great blog you have, i am doing a study on this subject and i fund some great information on your site

Thank you for that

Gijpie

I have to agree with anonymous chris , who cares it was a great bit of television, if you wanted it to go further then stick a bigger rocket on it!!! More speed = more distance even I know that lol

THOSE OF YOU AT THE END SURE MISS WHAT THIS FORUM HAS DONE. IT HAS BROUGHT TOGETHER SOME GREAT THINKERS, AND HELPED EDUCATE US COMMONERS AND ALSO TO LET US KNOW THERES ALOT MORE TO IT THEN JUST STICKING SOME ROCKETS ON TOP OF A CAR AND IGNITING THEM. I'M ABOUT 100% POSATIVE THAT THE AVERAGE JOE COULDN'T PULL THAT OFF AND GET THE CAR TO LAND WITHIN 5 METERS OF WHERE THEY PROJECTED. AND ITS FORUMS LIKE THIS WHERE NEW IDEAS ARE FORMED. FOR THE MOST PART WERE AT A SLOW IF NOT A STAND STILL OF NEW IDEAS IN OUR WORLD. KEEP IN MIND WE ARE DUE FOR A NEW TECHNOLOGY WHEN IT COMES TO TRANSPORTATION. ANYONE IN THERE 30'S REMEMBER SEEING THE SILENT BLACK AND WHITE FILM OF PEOPLE RIDING FLYING MACHINES OFF A PIER MANY YEARS PREVIOUSLY? IF I'M CORRECT IT WAS AN EARLY CONTEST TO SEE IF ANYONE COULD BUILD A MAN POWERED FLYING MACHINE.WINNER OF THE CONTEST WINS A FREE SUBSCRIPTION TO POPULAR SCIENCE AND 200 BUCKS OR SOMETHING LIKE THAT. AS FUNNY AS THE CONTRAPTIONS ARE A WINNER WAS PRODUCED. IN JR HIGH WE HAD AN EGG DROP CONTEST. OTHER SCHOOLS HAS A CONTEST TO SEE WHO COULD KEEP ICE FROM MELTING THE FASTEST. ALL OF THESE ARE TO GET THE JUICES FLOWING IN OUR MINDS AND TO SEE NEW PERSPECTIVES OF OUR YOUTH. NEVER DISREGUARD FORUMS WHERE PEOPLE DISSAGREE. THATS HOW THINGS COME TO LIFE.

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