Loop the Loop a

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Loop the Loopa Fifth Gear stunt special

• Hugh Hunt
• Cambridge University Engineering Department

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Simple physics
From A to B, conserve KEPE mgh ½mV12 so
h V12/2g 5R/2
G-forces are V2/R At B 5g g 6g At C
g g 0
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• bad assumptions
• particle
• no friction
• rigid suspension
• perfect tyres
• short wheelbase
• G-force not important
• ignore transients
• engine not powering
• planar no steering
• rigid structure

Fifth-gear Stunt Special R 6m ? V1
17.2 ms-1 (39 mph) V2
7.7 ms-1 (17 mph)
and G-force at B 6g
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Optimum shape for the loop (not a circle!)
It all depends on the criteria. For these
rollercoasters, height is not an issue.
Fifth-gear could have constructed such a shape,
but it would somehow have been less
impressive CONSTRAINT entry and exit
horizontal and coincident
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Steering
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Transient What happens to the suspension and
tyres when the weight of the car goes from 1000kg
to 6000kg ? Here is a notional graph of the
motion of a simple vehicle subject suddenly to a
change in g to 6g . The tyre and suspension
behave non-linearly.

1/6 ? The
suspension bottoms out, the vehicle grinds out,
the tyre blows out all pretty undesirable.
solutions stiffen suspension
increase tyre pressure from 30psi to . ???
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Engine power and friction
Toyota Aygo 67bhp, say 40kW PE increase
110 kJ If time to complete loop 4.5 seconds
then engine provides 90kJ on the way up
Friction ? 1 , mean G-force 3g, energy
lost to friction 1000 kJ Conclude Most
important to avoid grinding out friction
(even as low as ? 0.1) may cause the stunt to
fail.
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