Drag Coefficient

You can measure it. If you have a rendering (or really good picture) showing the front of the vehicle, then you can divide it up into rectangles and triangles in order to ease this computation. There are also programs that can do this automatically... or, they are easy to make (count pixels)

This depends on your tires. You can measure the rolling resistance of your tire if you have a ramp and a place where the wind is still.

It almost does. See the Mythbusters episode where they do this on a bicycle and don't have to break a sweat in order to keep up with a semi.

 

"A" is the frontal area, I think it's about 2.2 m^2 on the Prius.

For the Prius then, p*A*Cd/2 = 1.3 * 2.2 * 0.26 /2 is approx 0.37, and so the air resistance will be approximately F = 0.37 v^2 (v measured in meters per second).

The coefficient of rolling resistance varies with tire choice, tire pressure and the smoothness of the road surface, but it could be as low as 0.01. This means that that the rolling force would be about 170 newtons (assuming a mass of 1700 kg with about one or two occupants).

Solving when air resistance equals rolling resistance I get,

0.37 v^2 = 170
v^2 = 459
v = 21.4 m/s

This is about 75 km/h or about 45 MPH.

 

Urm, no. The variability you speak of is captured in the Cd term--no need to fake it into the Area term as well. Area is meant to be the real thing. (frontal equivalent cross-section, of course).

 

The area "A" is a bluff body frontal area. If you made a flat cutout having exactly the frontal silhouette of the car you have "A". As you point out, the aerodynamic drag from such a frontal area would vary depending on the shape of the body. This is the purpose of the Cd term: it adjusts the overall drag for the shape of the body, given the same area.

This is why saying a car has a good Cd does not necessarily mean that it has low aerodynamic drag. A car can have a low Cd but a huge frontal area, producing a lot of drag. This is also why some cars have less aerodynamic drag than a Prius, even though the Prius has a low Cd.

Tom

 

Yup, Cd is a factor that shows how much better a design is compared to a "bluff body" with the same frontal area. Think flat plate with smoothed edges or as Tom says, run the car though a panel and then make a copy of the hole with a flat panel. That's your "bluff body".

Best design so far is the French use of the boxfish shape. They got a Cd below 0.25 as I recall, with a car that was very useful as it was box shaped. Yeah it's ugly. Details details.

 

A bluff plate has a Cd higher than 1. A Cd of 1 represents the idealized case where the air (or other gas) is accelerated by the car's (or other object's) bluff shape to vehicle speed. Reality is messier.

Cd of a flat plate is about 1.28
http://www.grc.nasa.gov/WWW/k-12/airplane/shaped.html

 

The way I always think of it is that Cd is a measure of the slipperiness of shape, while A is measure of slipperiness of size. The Cd of a model Prius should be the same as a real car. Very useful for when wind tunnels were expensive and the only way to determine air resistance.

 

Don't forget that pesky Reynolds number.

 

You just need to use scale air.

Tom

 

Sometimes water is used in place of air when there is a big scale difference.

 

the Cd for car designers use is that for what is termed Flat Plate Drag. Its a measure of the percentage of a flat plate devoted to drag.

IMO its always been a bit deceiving, as the area of flat plate drag can be very different, as different as say a Honda Civic to a Prius. While the coefficient may be similar, calculation knowing the frontal area as a flat plate might be quite different. This is also true for parasite drag of aircraft, but in those cases 3 Views of the aircraft enable quick and ready assessments of the skin area of the plane.

I think I would prefer they played with the Cdo (total drag lbs) instead of the coefficient for which you need to be supplied with other data to work it out. With aircraft we can say at Vmax (maximum speed) thrust equals total drag (Cdo). Since thrust can be worked out, and the speed known, the drag figure is apparent. Cars however have contact with the road and rolling friction from that contact corrupts this simple working. And the CVT doesnt help either as we never really know what the gearing is

 

That is a rather remarkable claim. Please show us a credible source for it.

 

a measure of the percentage of a flat plate devoted to drag

yes I did write it a little awkwardly

while the raw number isnt directly representative, the coefficient is a description of how efficient your area of flat plate is in moving through air.

The flat plate has the same profile drag of the entire car, and assumes that 90% of the flat plate area has a Cd of 1.0, this is why 100% of the flat plate area is said to be more than a Cd of 1.0, Im a little rusty but I think I recall 1.17 as a rough cut dependent on the downstream shape.

Importantly. it isnt a number as some people seem to expect, that is a cardboard cutout of the frontal area of the car, this is a common misunderstanding

edit: oh you wanted references well
one of my favourite books is 'The Design of the Aeroplane' by Darrol Stinton, Modern Subsonic Aerodynamics R.T. Jones and I have other works by Martin Hollmann, RW Hovey

 

air is a fluid

 

At subsonic speeds air behaves very much like an incompressible fluid. At transonic speeds and higher compressibility becomes a factor.

Tom

 

That's a difficult way to say it. I worked at the same company with Martin Holman for a few years (I think he was consulting there) and took a couple of classes from him. I would be surprised if he explained Cd that way, he was a good engineer. Off topic, but I think I still have a pre-publication copy of part of his Composite Aircraft Design book that he used in our composites design class.

Cd of 1 is when the drag = the force required to accelerate the amount of air defined the frontal area of the car to the velocity of the moving body. Cd of 1 never happens that way in the real world but that's how Cd is defined. Set Cd in the drag equation below to one and do a dimensional analysis and it becomes obvious.