Think of the Coefficient of Drag the way you read the energy labels on appliances. Using an energy meter, I determined that actaul usage patterns have a great deal of influence on energy use, and it can vary greatly with the label. For instance moving my older fridge out of the kitchen and into the basement and using it as a “beer fridge”, the consumption was only one half of what was on the label.
However, when purchasing new appliances, the Energuide label is a useful tool in comparing energy use. Our Kenmore 22 cubic foot fridge bought 4 years ago has a consumption of only 550 KWH per year. Going through an old Sears catalogue of the 70s, when they published energy consumption figures, show a similar Kenmore 22 cu ft fridge consuming 2200 KWH per year!!!
So, when buying a new car the Cd is also a useful comparison tool.
@same
Let me add my intent…
It wasn’t just your comments, which I may have misread, but what seemed to be a general consensus that a so called, coefficient, can’t vary…and can’t be a variable. The mere indication that it is illustrated by Cd, letter(s) and not a number. implies that it is a variable.
That is how I approached the idea of correcting the statement " that a Cd is a coefficient and therefore, can’t vary." Being a coefficient has nothing to do with determining variability. If it did, we must then call it a " numerical coefficient". A numerical coefficient IS constant. A “coefficient” in physics, just indicates that once determined, it can be used literally, as a factor in determining related properties or relations. To say "a coefficient is a multiplier for a variable " further tells me that maybe that person still feels Cd can’t be a variable itself. I would say, “it can be a factor …in physics.” with the undertanding that factors can be constant or variable.
I have friend who is a department head in engineering who talks way over my head in engineering, but when he talks math concepts, he sometimes needs a little reminder like " did you really mean what you just said ? " to which he smiles and replies…“well no, not really.”
Road & Track magazine once had an article on drag, and the Cd. They explained it was the air resistance of the car compared to the resistance of a flat square vertical surface of the same cross sectional area, which has a Cd of 1.0. However, I forgot what the speed was at which this was measured, since air resistance rises very sharply above 60 mph.
@Docnick, that’s not quite right. I’ll give it a try:
Drag = 1/2 x air density x velocity squared x coefficient of drag (Cd) x frontal area
As has been pointed out earlier, Cd is derived from wind tunnel testing on car shapes, and it is relatively constant for a given car over a wide range of car speeds. If your car were going Mach 1, yes, its Cd would be different. But for, say, 0-100 mph, it’s pretty darn constant.
That’s the beauty and utility of the Cd as a number. Even though dynamic pressure due to the velocity squared term changes radically as your car speeds up, the Cd does not. Drag increases as the square of the velocity, but the Cd doesn’t change unless the shape of the car is physically altered, or fairings, etc, are added.
So the Cd is (for our purposes) an essentially unvarying number that tells us how efficient any given shape is at moving through a fluid. The only way to vary it is to change the shape ( or in the case of cars, add fairings, remove protrusions, etc, etc).
A flat plate has a Cd or around 1.3. Cars may have Cd’s in the .2-.3 range. So a car will have about 1/5th the drag of a flat plate with the same frontal area.
Here’s a useful graphic: zhttp://www.grc.nasa.gov/WWW/k-12/airplane/shaped.html
Yes, just pointing out that a flat plate does not have a Cd of 1.0. Its more like 1.3.
So Cd is derived by measuring drag in a wind tunnel, multiplying by 2, and dividing by velocity squared, air density, and frontal area. If you do that for a flat plate, you get about 1.3. For a car, you get about .2-.3.
I’m sorry, guess it wasn’t obvious I was being somewhat tongue-in-cheek.
Ideally, CdA would be a constant: Drag = 1/2[rho] v^2(CdA), with everything but velocity constant. Realistically, it varies, which is why wind-tunnel scale models can only be so accurate.
"which is why wind-tunnel scale models can only be so accurate. "
Very true. But I was surprised to read in a radio controlled aircraft magazines how similar model aircraft handling characteristics are to the real thing (stability, stall behavior, that kind of thing).
Actually dag, it wasn’t me that said a coefficient can’t be a variable. All I said (I think) was that the “C” in “Cd” is, by definition, a coefficient. A previous poster had said it could not be a coefficient because it was a variable, and it was to him I was replying.
Regarding the question of scale models not being exactly accurate, I have an analogy. Years ago I handcrafted a scale model of a log cabin for a close friend, complete with a working fieldstone fireplace. The first time I lit a mini fire in it, I realized that one cannot scale down fire. I got a single, temporary (VERY temporary) flame, but that was it. It simply did not burn like a fireplace fire.
The same principle applies here. The molecules in the air are a fixed size, and their interaction with surfaces is different in full scale than it is in model scale. Similar, but not the same.
Water, another fluid, changes its turbulence based on its viscosity. I saw an experiment where a wind up fish was put in a small tub of water. It swam realistically across the tub. An additive was added to increase the viscosity, and the fish was would up and put back in. It simply sat and wiggled, not moving across the water at all. The change in viscosity changed the way the fluid interacted with the fish’s motions.
The way Reynold’s number was explained to me, the smaller you scale, the “stickier” the fluid in question behaves…which is why insects can walk on water.
(From my physics class, a “coefficient” IS “unitless.” So, when you’re doing math, and you need to double-check that the answer is expressed in “N m/sec,” any coefficients will not have any units to cancel out.
So, if Cd varied with velocity in any predictable manner, it’d stand to reason there’d be a (m/sec)^-4 in there somewhere…)
The Smart For Two is a death trap for other reasons also. I was just voted the ugliest car to be caught dead in. It beat the Pontiac Dumpster/Aztec, Nissan Murano Convertible, PT Cruiser, HHR and others.
Its a death to your reputation.
@tsm,according to my schooling,most of the fishes propulsion comes from its body rather then its tail,plus its covered with slime,but you made a very good point,size does matter!-Kevin
That’s true, Kevin. And size does matter. All other things the same, it takes more energy to make a bigger hole through a fluid. I think the reason some people get confused is because there are other things that matter too. A properly designed larger body can have less resistance than a poorly designed smaller body. Size (actually more properly called for these purposess “frontal area”) is only one variable.
I like to think of the two major factors as size and turbulence, although turbulence is actually more of a byproduct of inability to cleanly move fluid rather than a factor in itself. Focus on reducing frontal area and eliminating turbulence results in efficiency in moving through fluids. I realize that this is a simplification; pressure waves can be used to manipulate turbulence, so it gets complicated.
