Sanity checking a striking claim
Posted by apgaylard on September 21, 2008
Interpreting technical data can be a tricky business, as demonstrated by an interesting article in last week’s New Scientist magazine. In a fascinating review of the recent progress made by manufacturers of electric cars the journalist tripped up in his discussion of the aerodynamic drag figures claimed for the Aptera, a two-seat electric car (the word refers to wingless insects – appropriate enough as the car does look like someone has pulled its wings off!).
“…the entire vehicle has a drag coefficient of just 0.15 – making its drag roughly the same as that caused by a single large wing mirror.”
This is a very striking claim, however, we shall see that some simple maths and a few estimates are all that is needed to show that the journalist has made a mistake here.
First, it seems that the journalist has confused the non-dimensionalised drag coefficient (CD) is with the drag force (FD). The drag coefficient provides a convenient way of comparing the relative merits of the shape of bodies of different sizes that may be travelling at different speeds (or even through different fluids). It is defined as:
CD =FD /(½ρV²A)
Where FD is the drag force (resistance of the fluid to the motion of the body); ρ is the density of the fluid (air); V is the speed of the body through the fluid and A is the projected frontal area.
For the car to have the same drag force (at the same speed, in the same fluid) as a wing mirror then the product of the drag coefficient and projected frontal area, the so-called drag area (CDA), of each body must be equal.
CD-car × Acar = CD-mirror × Amirror
With this understanding it is immidiately obvious that the statement is wrong: any driver knows that wing mirrors (more usually called door mirrors these days) are very much smaller than the smallest cars! So this equality is not going to work out; even accounting for the Aptera’s remarkably low CD (for comparison the best standard saloon cars have drag coefficients around 0.26)
It’s always good to get quantitative. There is a problem with this as I don’t know the projected frontal area value for the Aptera – so I’ll use a very generous value of 1m² (it keeps the maths simple!). I also happen to know of a relatively large (in the European context) SUV mirror with a projected frontal area of around 0.04m². This means that the Aptera’s frontal area is at least twenty-five times times greater than a typical large European mirror! For our drag area equality (CDA) to work out, so that the car and the mirror have equal drag forces acting on them, the mirror would have to have a CD twenty-five times that of the Aptera: 3.75!
This is out of the question: a flat plate sitting perpendicular to an air flow will have a CD of around 1.2; any automotive mirror is going to be much more efficient than that! A more reasonable approximation might be a hemisphere, this will probably have a CD of less than 0.4. So there’s no way that this will work out.
Given the huge difference in projected frontal areas, playing with wing mirror size will not produce a CDA that will save the journalist’s blushes: for instance, taking a CD of 0.4 the mirror would still require a frontal area around nine times the value that I’ve used. Again, this is just not plausible.
The moral of this story is that technical data can be tricky, particularly if it’s outside our usual experience – so it’s always best to do some simple sums and make some reasonable estimates, to ‘sanity check’ striking claims.
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