# Automotive Formula 1 Upside Down Question

1. Aug 8, 2012

### herrherrlich

Hey everybody, first ever post here on the forums. Read a few of the threads so far and have been very entertained so far.

My question stems from a debate I had with a friend while taxiing out to the runway and got quite heated. So much though, that I think we may have irritated the entire cabin within earshot of us. It is a take-off of the old 'Upside Down F1' topic. Here is the scenario:

An unlimited resources investor actually puts this to the test and develops a track with miles of flat, straight real estate to work with. A track is constructed that allows the F1 car to get up to speed, create the necessary downforce and then provide a corkscrew gradual enough to maintain enough forward and angular momentum to complete the upside down test. The track levels off perfectly inverted and the F1 car remains planted upside down on the track at speed.

Now, IF the investor runs out of money and the track abruptly stops... Initially, does the F1 car fall to the ground due to gravity and wind resistance -OR- flip upwards towards the sky do to forward momentum and residual 'net downforce'?

My position was that the 'net downforce' would flip the car skyward - at least initially - and I would LOVE to rub some math in his face the next time this topic comes up.

2. Aug 27, 2012

### LJW

Probably a small amount of lift (upwards downforce) raising the car slightly. Air resistance is very high at those speeds and without being powered the car would very rapidly slow down, lose downforce and come back to Earth.

3. Aug 27, 2012

### Ranger Mike

neither...once ground contact is lost so is all aero and the car will tumble uncontrolably to a crash. Without the tunnel effect of channleing air under the car and over the splitters . spoilers etc...you have no down force and are riding a 200 mph brick..those huge tires are over 40 % of total aero drag.

4. Aug 27, 2012

### Mech_Engineer

While it may have a net force pushing it skywards the instant it leaves the track, RangerMike's assertion that it will just tumble is probably right. As soon as the angle of attack of the spoilers changes any small amount the car will tumble and (probably) break-up. Watching any F1 crash where the car gets some air under the front end and immediately tumbles up into the air is good proof of this.

5. Aug 29, 2012

The vehicle would tumble, after slightly rising, almost immediately. This is due to the fact that the front wheels must leave the road surface first. Once the normal force from the from axle is lost, there is nothing preventing the front end from accelerating in the y (up) direction. A non-zero moment will be created about the contact patch of the rear tire. As the vehicle then rotates upward, a rather large angle of attack will result. This will yield an even greater moment about the rear axle. By this time the rear wheels have left the surface. So the car has already begun to tumble uncontrollably before it has even fully left the road.

Now, if we want to really do a mind experiment, we must make the engineering assumption that the road instantaneously falls away (or rises away depending on your coordinate system). At this time a free body diagram can be made of all the forces acting on the vehicle. In the x direction, only drag remains, thus the vehicle must slow down. F=ma, where F also equals area*drag coeff.* vel^2*density*0.5. Divide this value by mass and we have acceleration in the negative x direction of course. That's the easy part. What we are really concerned with is forces in the y direction. For simplicity, let us also assume that lift is equal to mass*g. Ok, so now your thinking that it will fly until it slows enough to reduce lift. However, the placement of the forces is just as crucial as the magnitudes. Unless the sum of all the aero lift passes through the center of gravity, a moment will be created. This is called a force couple.

I do not know what type of lift forces the wings and body create in free space. But we can make more simplifying assumptions. We know that the greater the normal force, that greater the frictional force. the greater the frictional force the greater longitudinal acceleration. So I will assume that the rear wing produces much greater lift than the front. Also F1 rules dictate a weight distribution very near 46/54 front rear. Almost 50/50, so the center of g is split halfway between the axles. Since we have assumed lift is not distributed 50/50, we can make the educated assumption that a force couple is present and the vehicle will rotate and tumble out of control.............

Then again, anythings possible...............lets test it!!!!

6. Aug 30, 2012

Jeez Rob, I think you went a little more complicated than what he was after, but hey...

It's kinda like why helicopters have hinges on the rotary wing, the blades create more lift on one side of the aircraft, thus crating a moment about the centre of gravity. The hinges compensate for this affect and if they weren't there, the helicopter would just tumble to the ground.

7. Aug 30, 2012

Yes, I think I remember a modern marvels episode on helo's that discussed that very problem early on in the development of helo's. Damn I love that show~!

8. Aug 31, 2012