
Quattro Reeling in Free Wheelie 
So
it was back to Reading last Monday with the new UJ bearings fitted to Quattro.
This time, I left off the spats and locked the rear steering.
Keith
and Chris from Wycombe Abbey School met Jim and I there as we were planning to
do some tests on the Greenpower car (Free Wheelie) at the same time. We were
also met by Graham SpareyTaylor who was hoping to have his Quattro there but
unfortunately ran out of time to complete the latest modifications.
The
tests we can do at present are still not very scientific but the bottom line is
“how fast does it go mister?” Well the answer is a bit faster than last time.
The weather conditions were much better with a temperature of about 24deg and
very little wind. I was able to maintain 30mph (48kph) reasonably comfortably
with a number of laps at 32mph (51kph) and after a pep talk from Dr Graham a
sprint lap at 35mph (56kph)!
At the
very beginning of my Quattro development, 35mph was the magic number that I was
trying to achieve as a racing speed. This is generally about the average speed
of the winner (Steve in the Beano) of most BHPC races. Unfortunately one fast
lap around Reading Velodrome is not the same as a 40 minute race on a twisty
cycle racing circuit but at least it is a step in the right direction.
Forgive
me for the next bit, as it is largely a repeat of my original Quattro article
for our club magazine but with some of the numbers updated.
The
power required to maintain 35mph is made up of two main elements.
Air
Resistance Power = CdxA x½ρV³
Where
Cd is the drag coefficient, A is the frontal area in m², ρ is air density
(1.2kg/m³ at 20°C) and V is the speed in m/s.
Rolling Resistance Power =CrxVxN
Where
Cr is the rolling resistance coefficient, V is the speed in m/s and N is the
normal force in Newtons (kgx9.81) on the tyre.
There
are other mechanical losses such as bearings and chain friction but these are
small and I will ignore them in the following examples.
35mph
Beano Power
The
Cd for the Beano is probably about 0.12 taking into account gaps, wheels etc.
The frontal area is 0.35m².
Air Resistance Power = CdxA x½ρV³ gives 0.12x0.35x0.5x1.2x15.5³ =94W
The
Cr is about 0.006 for good cycle tyres, Steve weighs about 65kg and the Beano
about 17kg giving a total weight of 82kg.
Rolling
Resistance Power =CrxVxN gives
0.006x15.5x82x9.81 =75W
Therefore
Steve needs to put out about 169W to maintain 35mph in the Beano.
35mph Quattro Power
The
frontal area of Quattro is about 0.6m². Let us assume the drag coefficient is
the same value of the Beano at 0.12.
Air
Resistance Power = CdxA x½ρV³ gives
0.12x0.6x0.5x1.2x15.5³ =160W
If I was to use my
Solidworks CFD drag figures of 6N at 15m/s this would give only 90W which I
don’t believe, as there is no account for gaps, rotating wheels etc. More on
this another time.
Again
assuming a Cr of 0.006, I weigh about 76kg and Quattro weighs 34kg giving a
total weight of 110kg.
Rolling
Resistance Power =CrxVxN gives
0.006x15.5x110x9.81 =100W
This
makes a total of 260W which is the high end of an attainable figure for me and
gives an idea of what I am up against!
35mph
“Upright” Racing Bike
Putting
things in to perspective, a racing cyclist in a crouch position has a frontal
area of about 0.3m² and a Cd of 0.9.
Rolling
Resistance Power =CrxVxN gives
0.006x15.5x82x9.81 =75W
Air
Resistance Power = CdxA x½ρV³ gives
0.9x0.3x0.5x1.2x15.5³ =603W
This
makes a whopping 678W!
Greenpower Car Tests

Free Wheelie at Reading 
The Greenpower
events are aimed at secondary school children, are all four hour endurance
races and are generally held at motorsport venues around the UK. All teams have
the same motor and six 12 volt batteries to be used in pairs. During the race
at least five team members must drive the car, and up to six further members
can act as pit crew. Other than the motor and batteries, teams are free to
design a car from scratch, or build one of the kit cars. All cars must follow a
set of strict safety regulations but there is quite a variety of designs sitting on the grid before a race.
http://www.greenpower.co.uk/

Free Wheelie's First Race at a Soggy Silverstone 
The same
equations can also be applied to Greenpower Electric Cars but at the moment the
target speed is 25mph (40kph) for the Wycombe Abbey School car.
25mph
Free Wheelie Power
Again
there is a bit of guesswork for the Cd of Free Wheelie but it is probably about
0.25 taking into account gaps, wheels etc. The frontal area is about 0.35m² and
the speed is 11m/s.
Air Resistance Power = CdxA x½ρV³ gives 0.25x0.35x0.5x1.2x11³ =70W
At
the moment, the car is fitted with 16” (349) Schwalbe Marathon tyres. These were
one of the tyres tested by John Lafford. http://www.hadland.me.uk/rolrec10a.pdf He found they had a Cr of 0.01, Keith weighs 80kg and
the car about 95kg giving a total weight of 175kg.
Rolling
Resistance Power =CrxVxN gives 0.01x11x175x9.81 =189W
This
makes a total of 259W.
So
it seems that at 25mph the rolling resistance is dominant.
If
the tyres were changed for ones with a Cr of 0.006, and the weight reduced with
a 20kg lighter driver, the rolling resistance power could be reduced to
0.006x11x155x9.81=100W.
As
can be seen from the Reading picture, teacher Keith is a little large for the
car as it is designed for smaller and lighter young ladies. His shoulders are
causing extra air drag and a pupil would probably weigh 20kg less.
The
aim of the trip to reading with Free Wheelie was to find the optimum gear to
use at the next race. Greenpower cars have the opposite problem to human
powered vehicles in that, the motor spins at about 1850rpm rather than the
90rpm of leg power. To get the correct
wheel speed, the car has a 14t freewheel on the motor and a 5 speed block on
the axle with 47t, 50t, 53t, 57t and 62t sprockets which are selectable with a
standard rear mech. At the moment, the gear ratio is selected before the race, based
on battery capacity, race conditions and duration; it is not touched during the
event. Most of the circuits are flat and the motor becomes horribly inefficient
if it is run too slowly, which would flatten the batteries before the end of
the race.
The two
12V batteries can provide about 17Amps to the 24Volt motor for the 80minutes
before they are changed. This gives a motor input power of 24x17=408W, taking
off a bit for controller, contactor and wiring losses probably leaves 400W.

Motor Performance Graph 
At
17Amps, the motor is running at about 73% efficiency, which is near its peak. This
means there should be 292Watts at the output shaft.
Working
backwards from this power, using the same equations, with a lighter driver and better tyres (0.006), gives a theoretical speed
of 14.5m/s or 32.4mph (52kph) with the rolling power at 132W and air power at 160W.

Splashing About at Silverstone 
The next Greenpower event is on Sunday 10^{th}
June at Goodwood Motor Circuit and the aim is to complete the four hour race
without any major breakdowns or flat batteries. The team will be using the Schwalbe
Marathon Tyres and starting on a low gear. The gear could be increased at the
first battery change, depending on the battery condition.
I'll not be there, as I am going to be splashing
about at Fowlmead in the World Championships. The weather forecast is not very
good, which is a shame but in Quattro, it may give me an advantage over some of
the bikes.