[John]

Since I plan on using my vehicle for a work commute most of my driving will be at 100 km/h. Aerodynamics will have a significant impact on the range of the vehicle. Whatever I do needs to be light weight as my vehicle will also be a bit weight challenged and operating quite close to it's GVWR. I'm considering degrilling the front (no point in all that cooling drag without an ICE), fitting a belly pan just under the engine (motor) compartment, fitting skirts to the rear wheel arches and turbulators over the rear window. I will try to verify each aero mod as an improvement somehow such as steady state motor amps on a known piece of road in calm conditions. The function of the turbulators could be verified by taping a ribbon to the roof of the car and driving down the road with a chase car to monitor the behaviour of the ribbon. A full belly pan would certainly help the aerodynamics but would weigh quite a bit.

 

[John]

One way to minimise you cooling air requirement would be to duct it from your cold air intake at the front of the car to where it is needed. I would say the majority would be needed by the motor. Those with direct drive would even benefit from fan assist for this particularly when travelling slowly up hills. I have a liquid cooled controller so it will be easy to duct air to the tiny little radiator. Those with air cooled controllers could build a shroud to duct air over the heat sink where it is needed.

I'm thinking about making circular ports at the stagnation point on the front bumper passing into a conical diffuser designed for maximum pressure recovery dumping into an air box to slow the flow and allow dust and water to fall out and drain away. The ducting would connect that air box to the motor and controller.

Even with a belly pan under the entire engine compartment there would still be openings at the transmission tunnel and drive shaft and steering rack ports without needing to create special vents through the pan. I suppose I could duct the hot air from the motor out of the compartment to prevent it elevating the temperature. Then I would only need to supply a tiny amount of ventilation air to the compartment to remove a small amount of heat and some hydrogen from the batteries.

 

[John]

Placing the ports at the stagnation point will cause the stagnation point to move somewhere else on the surface. My theory is that by putting the ports there (basically at the apex of the vehicles shape) the flow will have travelled the minimum distance across the surface of the vehicle possible before entering the port causing minimum boundary layer growth for maximum diffuser efficiency and pressure recovery.

 

[John]

What you’re talking about is an NACA submerged scoop. They don't suffer from the loss of efficiency you would expect from a regular scoop due to it ingesting the boundary layer. Something about a vortex generated by the flow over the leading edge of the NACA scoop ejecting the boundary layer and causing it to ingest clean air.

Boundary layer growth might be greatest at the stagnation point but the boundary layer would be thinnest at that point due to that being the first point of contact of the airflow. Placing an intake there wouldn't cause an increase in boundary layer growth. First air flow contact would simply move out to the edges of the intake.

 

[John]

I've been wondering about the effect of the incidence of the belly pan to the road. The belly pan slopes down from the front towards the road. This would cause the air flowing under the car to accelerate towards the back of the pan (to a rearward velocity relative to the road) which would in turn cause the pressure to drop below atmospheric pressure sucking the pan (and the car it's attached to) towards the road. The down force generated might have a negative effect on the overall aerodynamic drag. If the belly pan wasn't ridged enough the effect would exaggerate it self as the pan flexed towards the road. The high velocity flow is then dumped when it reaches the back of the front axle into a large open bottom cavity formed by the rest of the engine compartment where it mixes with dead air. There is then no chance of diffusing the flow to pick up some forward pressure to mitigate the drag.

I think Kevlar would be a better choice for a pan than carbon fibre. It has a similar strength to weight and is much tougher it is just not as ridged.

 

[John]

I was thinking that effectively dumping the high velocity flow into a large cavity containing dead air would prevent the low pressure area from going further back than the back of the belly pan and would reduce any up wash effect. Pressure recovery in this area without a diffuser would be quite poor don't you think.

I would prefer the notion of not creating any negative lift. My car also has sloping front pan. I'm guessing it was built that way for a clearance angle for steep driveways and the like.

 

[John]

Your lower front bumper (spoiler) doesn't appear to have a very pronounced lip. I imagine it would spill quite a lot of air into the underside flow especially considering how flat over all the front of the vehicle is with a lack of tapering off at the corners.

 

[John]

A lot to do with aerodynamics is counter intuitive. A stream of flowing air possesses a few different forms of energy. The dominant forms to consider are pressure energy (also known as flow energy) and kinetic energy as they are flow dependant. As the kinetic energy increases due to the flow accelerating to a higher velocity the pressure energy decreases and the converse is also true. The air duct formed by the underside of the belly pan and the road decreases in cross sectional area at the back forcing the flow to accelerate to pass the same volume of air as it must this in turn causes a reduction in pressure via this energy exchange.

 

[John]

To elaborate further the laws of the conservation of energy and the steady flow energy equation apply. The two energy forms considered are kinetic energy and pressure energy due to the dynamic exchange of form that occurs between the two due to the conservation of energy.

Work is defined as equalling force times distance (f.d), in SI units Newtons times Meters (N.m or a Joule).

Power (watt's) equals work per time (f.d/t). You will recognise (d/t) distance per time as being speed so power also equals force times speed (N.m/s).

Energy equals power multiplied by time (W.h, watt hours) or (f.d/t.t) so time cancels out of the equation so it ends up as (f.d) or the equivalent of work which in SI units was Newton meters.

Newton. In SI units gravity will produce an acceleration of 9.81 meters per second per second (9.81 m/s/s or 9.81 m/s^2) or a force of 9.81 Newtons per kilogram (9.81 N/kg) so N = kg.m/s^2 (force equals mass times acceleration). This is what quantifies a Newton.

Kinetic energy equals half mass times velocity squared (KE=1/2.m.V^2). V=d/t so KE=1/2.m.d^2/t^2 or in terms of units KE=kg.m^2/s^2 and substituting N for the term kg.m/s^2 results in KE=N.m. Carefull not to confuse mass with meters (both are m).

Flow energy equals pressure time’s volume. Pressure equals force per area so in terms of units QE=N/m^2.m^3. So this cancels down to QE=N.m. Flow energy is what does the external work in a hydraulic or for that mater pneumatic cylinder.

There ends the definitions and derivations.

Flow over curved surfaces.
An object in uniform rotary motion i.e. scribing a circular path at a constant velocity is in fact continuously accelerating toward the centre of the circle. There must be a continuous force pulling the object towards the centre of the circle. Fluid flowing over a curved surface at uniform velocity will similarly be accelerating towards the centre of curvature. The forces required to generate this acceleration will cause changes in the pressure at the surface the fluid is flowing over. Flow over a convex surface will require the air to accelerate towards the surface. This accelerative force will cause a reduction in pressure at the surface conversely a concave surface will cause a pressure rise at the surface as the air accelerates outward from the surface toward the center of the bend. This is why you get a pressure rise at the base of a cars windscreen. The bend in the flow there requires an abrupt acceleration outward from the surface.

 

[John]

I would love to see the results of such a test. It would vindicate or debunk the theory as to why the previous belly pan didn't produce a more positive result. It has occurred to me that there might be some other large airbrake on the truck which was making the gains a smaller part of the whole drag picture making the gains difficult to see.

To see what sort of down force you might expect I ran through a quick calculation with some guestimated values. Assuming sea level standard air density and pressure and a flow velocity of 60 mph (27m/s). Assuming the belly pan reduced the cross sectional area to half doubling the flow velocity. Using 1m^3 for flow volume.
KE1+QE1=KE2+QE2 so QE2=KE1+QE1-KE2
Density of air is 1.225kg/m^3 and air pressure is 101325N/m^2
QE2=(1.225/2*27^2)+(101325*1)-(1.225/2*54^2)
=99985
Pressure drop=101325-99985=-1340N/m^2
Assuming a belly pan area of 1m^2 and a uniform pressure drop across the length of the belly pan the average pressure drop would be half or 670N/m^2 for a force of 670N or about 68kg of down force. Note how small the pressure drop is, 1.3% of atmospheric pressure. This still generates significant down force.

 

[John]

To put this in perspective drag increases with the square of speed so if your top speed went from 55 mph to 57 mph that would be equivalent to a 7% reduction in drag or going from a cd of 0.45 (guestimated) to 0.42. Assuming that the aerodynamic drag makes up about half of your total drag, by driving at a similar speed as before you could convert that into approximately a 3.5% increase in range. Top speed is not a particularly fine measure of the gain. I'm not sure what would make a better measure.