[mattW]

Ok I don't think I'm understanding this properly, as far as I know force occurs due to a pressure differential and a sloping belly pan would have positive pressure since it would be deflecting air downwards, and since there would be less pressure across the bonnet (/hood) and behind the pan the total force would be upwards and backwards. I try to explain my understanding of it visually in this dodgy flow diagram attached, the green line is where i would image the force to be acting. Is there something I am missing? what would be creating down-force?

 

[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.

 

[mattW]

I understand how that would work with a gust of wind at the front of the car; Pressure would build at the front compared to the back but then the pressure difference would 'suck' the excess air from the high pressure to low pressure zone. But when the car is moving the pressure at the front of the car is being constantly renewed by new air crashing into it. The only reason the air would accelerate would be because the pressure differential was maintained which means that there is still high pressure at the front. I'm not trying to argue, I'm just struggling to understand how it works...

 

[Greenflight]

Matt, try thinking of it this way (and please, somebody smack me upside the head if I'm getting this wrong).

Every action has an equal and opposite reaction. So each time the car acts upon the airflow to change it's direction, a force is exerted on the car as well as the air. So when the car deflects air upwards, the air exerts a downward force on the car, and vice versa. And each action/reaction takes energy. So even if the net force is zero, if the air has to go up and back down, it takes energy.

When working with air flow at subsonic speeds (I think we can all agree that this is subsonic) it is generally considered incompressible. This is not to say that air is incompressible- it's just that the effects of compression in these situations are small enough they're worth ignoring.

So anyway, when the air passes under the car, the belly pan deflects it downward (note energy loss) and then flattens it out (note energy loss). As John was saying, this reduces the cross sectional area of the "tunnel" underneath the car. Since the forces aren't enough to compress the air a noticeable amount, the only option the air has is to speed up.

Think of it as the proverbial water in a pipe. If the pipe becomes smaller, the water speeds up. Same diff.

And as far as the air behind the belly pan, it becomes a tremendously disorganized flow that my feeble mind can only guess at.

Way not to speak to the question, huh?

And BTW, thanks for that glamorous pic of my truck. To be honest, I never really looked at it that way before.

 

[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.

 

[Greenflight]

OK, so here's what I'm thinking of wasting duct tape on now.

Check out the pics of this car (BTW, the batteries in this car are AMAZING): http://www.austinev.org/evalbum/464

See that front bumper? I'm thinking of rigging up something like that. I would be able to lower the bottom edge of the bumper, reducing the amount of air that passes under the car, and also duct it further out to the sides, away from the front wheels. I could also bring the front of the fender closer to the wheel, reducing the excessively large gap that currently exists. I could also flatten out the belly pan quite a bit.

Plus it would be really easy to test out.

So, what do you guys think?

 

[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.

 

[Greenflight]

That's a noticeable effect. Very interesting.

I'll probably work on the fairing tomorrow if I have time. We'll see. I can imagine reducing the overall flow underneath the car by that much would help quite a bit.

I'll post the results when I'm done duct taping.

 

[mattW]

Hey guys I was thinking we could start a Wiki topic about aerodynamics. One section on the theoretical side of things and the other on practical projects for people to undertake. I just realised that this topic is approaching 50 posts and appreciate how much information is on here, it would be good to get it into an easily accessible form. Would you guys be willing to add some of your wealth of knowledge?

 

[Greenflight]

Woohoo the 50th post is mine!!!!

Good idea Matt. I'd be happy to add some pics of my experiments, along with results, etc., as long as I could figure out how. Never actually used a wiki before.

 

[Greenflight]

OK, I had some time to kill today (finally), so I started working on a bumper cover for my truck. As soon as I can get it to the point where I'm confident it will withstand 50 mph winds, I'll try it out.

I'll post some pics of this ridiculous looking contraption as soon as I get the chance.

And I keep meaning to add to that wiki but I can never seem to get around to it!

 

[Greenflight]

OK guys, here's the final rendition (sorry for the bad pic). I decided I wasn't comfortable having a huge chunk of foam on the front of the truck, so I made one out of lexan instead. Not the most elegant design ever, but hey- it works!

I might have picked up 1-2 mph. I should probably try making a new belly pan that attaches to this thing, rather than just "existing" behind it. But at any rate, the fact that it didn't slow the car down is a good sign.

 

[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.

 

[Greenflight]

Hmmm. 3.5%. That's kinda depressing.

Either way, this stuff is fun to play with. Plus I think it makes my truck a little more bearable for the people behind me.

Just because I'm curious- You seem pretty familiar with aerodynamics... Is that your line of work?

 

[mattW]

Hey guys, we're been doing all wrong, trying to make subtle changes while keeping with the style of the car... we should be ashamed. THIS is what we need to do:

And look at the European syling on the front here:

i'm...just...speechless!

 

[mattW]

But on a more serious note I just found a forum for people trying to up their mpg with a whole section on aerodynamics with 11 pages worth of topics. Check it out here, looks like a good resource.

 

[Greenflight]

Okay, don't know how I missed that post before, but I seriously almost fell out of my chair when I saw that... Do you know if the guy got any better mileage after, uh, "tweaking" it?

I like the rear hatch... nice touch.