So, how fast will it go?

One of the eternal questions, this one - along with one or two others that have cropped up over the centuries to derail civilisations, religions and marriages.

I asked this of other owners of over-engined Spitfires in the course of building mine and received answers up to 135mph without any evidence other than the credibility of the lone witness.

Observations of the theoretical top speed, based on gearbox, overdrive and final drive ratios and engine maximum revolutions are offered but do little to verify claims of real-world performances.  I have set about trying to attach some well-known science to this touchy subject and have put my findings down here.

The ultimate top speed of any vehicle is dictated by the phenomenon of drag. 

When all bodies move through air or water they generate a force which tends to slow them down (drag).  The size of this force is related to the “thickness” (viscosity) of the medium through which they move and the speed at which the body moves and the size of the body and the slipperiness of the shape of the body.

The viscosity of, in the case of land vehicles, air does not change for speeds less that the speed of sound.  Therefore this quantity can be considered as fixed.

The drag on a vehicle comprises two parts,

• One part is related to the rotation of the mechanical components of the vehicle and increases in proportion to the speed at which the components revolve.  This component is minimised by good mechanical design and tyres that are well pumped up.
• The other component of drag is related to the movement of the vehicle through air and can be felt as wind-resistance if you stick your hand out through an open window of a car travelling at speed.  This aerodynamic drag increases out of all proportion to increases in the vehicle speed.  Specifically, the increase in aerodynamic drag increases with the square of the increase in speed.

What does this mean?  Well, if you double the vehicle speed, say from 20mph to 40mph the aerodynamic drag will increase by four times (2x2).

For example, if the aerodynamic drag at 20mph is (say) 25kg, at 40mph (20x2) the drag will be 100kg (25 x 2x2). (please excuse the combination of SI and Imperial units here)

Similarly, if the speed is tripled the drag will increase nine fold (3x3).  The aero drag of 25kg at 20mph will increase to 225kg at 60mph.

Quadruple the speed from 20mph to 80mph the drag will increase by 16 times to 400kg.

Increase the speed by 5 times from 20mph to 100mph the aero drag increases by 25 times from 25lbs to 625kg.

So, for a five fold increase in speed from 20mph to 100mph the aerodynamic drag the vehicle creates which the engine has to overcome has increased twenty five times.

So far the value of aero drag I have used is only a guess for illustration.  There are some other features which need to be used to make an actual measurement.

One other feature which needs to be measured is the frontal area of the vehicle.  Obviously a vehicle with a large frontal area will need to push more air aside as it moves than one with a small frontal area.

The other feature which needs to be known is the drag coefficient (Cd) of the vehicle.  The Cd is a measure of the slipperiness of the vehicle’s shape and is often quoted by vehicle manufacturer’s advertising bullshit, more on this in a moment.

Internet searches have given the following values for Cd and frontal area which are relevant (plus many more)

Body or Vehicle	Cd	frontal area    (sq ft)	Cd x frontal area
Flat plate edge on	0.001
Wing section	0.005
3d teardrop	0.12
sphere	0.73
Flat plate face on	1.25
LeMans race car	0.3
Mini Cooper	0.52
’80 Spitfire	0.42	15.5 sq ft	6.5
’72 Stag	0.38	18.25 sq ft	6.93
’68 TR250	0.45	16.8 sq ft	7.57
Lotus 7	0.62	15.8 sq ft	9.81
Landrover 110	0.55
MGB GT (cf GT6?)	0.4	17.3 sq ft	6.92
Single seat race car	0.71 - 1.0 depends on “wing”
Motorcycle	0.5 - 1.0 depends on fairings

The aero drag is related to both the frontal area and the Cd of the vehicle.  Many motor manufacturers are proud to claim low values of Cd for their products but are usually very unforthcoming about the frontal areas of their vehicles to allow like-for-like comparisons of say a mini-people carrier and a saloon or hatch with the same number of passenger seats.  Anyway, this is getting away from this discussion.

So, putting together all these factors it is possible to show that

• the aerodynamic drag is related to
• the density of air
• the Coefficient of drag
• the frontal area of the vehicle and
• the square of the speed of the vehicle.

In SI units the aerodynamic drag in Newtons (unit of force) is related to vehicle speed in metres per second by the equation

Drag = ½ x air density x Cd x frontal area x speed x speed

At terminal velocity the power produced by the engine to drive the vehicle forwards exactly equals the aerodynamic drag pulling it backwards.  If you know the Cd of your vehicle, the frontal area and its maximum speed, it is possible to work out how much power the engine is applying to the road.

Further internet searches have given graphs ready plotted relating drag and power. I have reproduced one here which relates speed, power and aerodynamics to allow some comparisons.

The graph shows a family of curves, each showing the power required at the rear wheels to drive a vehicle at speeds between 100 and 150mph.  The lowest curve represents a vehicle whose Cd x Frontal area (Fa) in sq feet = 4, increasing by 2 each time up to a maximum of 20.

The Cd x Fa of a 1500 Spitfire is given as 6.5.  If we assume the power at the back wheels of a Spit 1500 is 50hp (a reasonable assumption) and that the Cd x Fa is 6.5, the point on the graph were the 50hp line and the 6.5 curve cross will give the terminal speed.  Close examination of the graph will reveal that the point where the line and the curve would cross is actually less than 100mph.  This appears to match practical observations.

If we now take some of the claims made by 2.5 litre Spitfire owners of terminal speeds around the 135mph mark and follow the Cd x Fa = 6.5 curve to 135mph, a requirement of something of the order of 125hp at the wheels is indicated.  125 wheel horsepower from a 150+hp engine appears to be a reasonable assumption and would appear to support these maximum speed claims.

Now to my car, 2.5 PI as per TR5 spec, I assume 150 bhp at the crankshaft and so 125 wheel horsepower (the rolling road at the Mallory Park Track Day will tell all, but I have no windscreen, no hood or hard top and lots of bits sticking out into the breeze - roll cage, my head, seat head restraints, Monaco headlight pods, spare wheel on the boot lid, etc, etc, etc.

I would guess at a Cd slightly better than a Lotus 7, give the wheels of the SuperSix are covered but the frontal area on my Spitfire based special is going to be greater than a 7.  I expect the Cd x Fa of the SuperSix to be comparable to a 7, i.e. 10 in round figures.

If you find the fourth curve up on the graph, which represents Cd x Fa = 10 and read off the terminal speed which equates to 125 wheel horsepower you will see that a maximum of 120mph is indicated.

I have been able to cross reference these findings with a graph relating Lotus 7 terminal velocity with maximum engine power.  That graph indicated a maximum 7 speed of 115mph with a crankshaft power of 150bhp, 105mph with 115bhp and 100mph with 90bhp.  These Lotus 7 values also appear to correspond with the figures obtained from my practical experience.

I have yet to exceed 110 (indicated) miles per hour.  Either my speedometer is inaccurate at these high speeds, or the engine isn’t as powerful as I hoped, or the Cd is greater than 0.62 or the overdrive top gear is too tall and maximum engine power isn’t reachable before increasing aerodynamic drag puts the brakes on.  Possibly a combination of all of these factors conspires together.

Either way, I have been able to satisfy myself that the claims of other 2.5litre Spitfire drivers may well be true, that the aerodynamics of my car approximate to those of a stalled brick sideways on and that 110mph in a car without a windscreen is far too fast enough!