## Can a Formula 1 car drive upside down? Can an ordinary car fly?

February 9, 2010The 2010 Grand Prix is about to hit Melbourne next month so this week, mathspigs we are going to look at car aerodynamics. There are two factors in car aerodynamics. Lift(L) and Downforce(D)

**LIFT (L)**

Car designers didn’t worry about aerodynamics until the sixties when cars could go fast enough to experience aerodynamic lift, which naturally, reduced tyre traction. Skirts are added to cars to not only reduce this lift but also create a ‘suction’ (Bernoulli Effect”) under the car.

Here is the Chevy ’69 Camaro from Camaro Untold Secrets. At 115 mph ( 185 kph which is not only fast but over street speed limits!!!!!) it experienced a front Lift (L) of 375 lbs or pound force.

We’ll simplify the aerodynamics and assume this graph is a parabola as follows.

NB: the only units to use in this equation are L (lb force) and v mph.

Once you know this equation you can calculate the velocity required for a ’69 Camaro to leave the ground due to front Lift (Assume once the nose lifts the downforce no longer applies ie. equals zero.)

We know the weight of the ’69 Camaro = 3,675 lb.

So mathspigs if the ’69 Camaro can go fast enough so that the front Lift equals its weight, it will fly! At what speed will ’69 Camaro fly?

**Downforce (D)**

The ultimate design in car aerodynamics is the F1 racing car. The Downforce (D) on the car is created by the front and rear wings, which work in reverse to aeroplane wings pushing down on the car) and the underbody gap which crates ‘suction’ by the Bernoulli effect.

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**Williams FW31 weight including driver 605 kg**

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** Renaut R30 total weight 605 kg**

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**Toyota TF 109 weight 605 kg **

** BMW Sauder C29 620 Kg**

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**Ferrari F60 605 kg**

Downforce is approx:

35% rear wing

25% front wing

40% defuser on underbody

While downforce equations are complex ( See Wikipedia ) they approximate to the following equation for a standard F1 car design:

**Could the Downfoce (D) on a F1 car exceed its weight so that it could drive upside along a … very long tunnel? I’m thankful to ****New Scientist**** (Aerial Glue 20 Jan 2010) for this insight.**

Now mathspigs you have the mass of F1 car above so you can calculate the speed at which a typical F1 racing car could drive on the roof of a tunnel glued to the ceiling by its own downforce.

NOTE: This equation only works for a limited range of car mass, m. You can’t reduce m by dumping bits of the car. Likewise, if you add bits to the car to increase m eventually the aerodynamic constant, k, will change.

**Does the weight of a driver make a difference? **

Mathspig did stand in the pits in the Australian Grand Prix in Adelaide in the ninties ( with a borrowed ticket) not far from Ayrton Senna (Right. Tragically killed in 1994) and I was shocked to see how small he was. His height is recored at 171 cm but that is Mathspig’s height and he was shorter. Today while some F1 drivers are over 6 ft (183 cm) including Australia’s Mark Webber (Right) most are not tall and, therefore, not that heavy.

When the KERS (Kinetic Energy Recovery System), which stores braking energy, was introduced 2009 drivers lost weight to accommodate system.

Nico Rosberg 76 kg to 66 kg

Kubica 78 kg to 70 kg

Heidfeld 56 kg to 59 kg

While Trolli, Hamilton and Vettel reduced their weights to 64, 67 and 62.5 kg respectively. More info

Typically, a driver will lose 5 kg just competing in a Grand Prix. IF the driver dropped 15 kg would that effect the upside down speed of an F1 racing car? Drop the mass (m) value above and see if it makes much of a difference.

Or, instead, if your School Principal was driving the F1 racing car ( Assume an average F1 driver weighs 65kg. How much heavier is your Principal to an F1 driver? Guess.) Increase the mass (m) in the above equation by this amount and you can calculate the speed at which your school principal and F1 car would drop off the tunnel ceiling.

**Meanwhile, even Mythbusters**** hasn’t tested this stick to the ceiling theory. Why?**

**Even the slightest bump on the ceiling could disrupt the underbody ‘suction’ and down goes the $zillion car and driver upside down and at speed.**

**This hasn’t stopped some Youtube mockups of F1 cars driving on the ceiling****!!!**

[…] for fun maths, for bringing the science of patterns into the real world, with problems like the downforce required to drive a car upside-down, or the number of balloons required to hoist a house (after […]

by The mathspig - porcine maths | Maths-Whizz-The Whizz April 8, 2010 at 11:52 amHi Mathswhizz,

by mathspig April 9, 2010 at 4:48 amGreat to hear from you and share our enthusiasm for maths. cheers Mathspig

thanks, in the second box what does k =? im guessing its a constant, but what is the value for it and does it change according to the car?

by ali boyer June 24, 2010 at 12:16 pmHi ali,

by mathspig July 12, 2010 at 6:50 amSorry about the late reply. I’m just back from a tour of Europe. Believe me anywhere in Europe is a long way from Melbourne, Australia. I’m trying to simplify maths for school level students. K is a constant. I wrapped a number of variables into that constant to create a workable formula. If you want more details you will find the full formula on the wikipedia reference in the post. Cheers mathspig

with its speed it can if the driver is good!

by discount sports tickets July 23, 2010 at 1:34 pm