# What does S represent in Chris Hadfield's D = ½ ρ v² S?

Retired test pilot, CSA astronaut and ISS Commander Chris Hadfield's new Master Class advertisement video Chris Hadfield Teaches Space Exploration - Official Trailer - MasterClass is heavily edited and I think mixes the explanations for several things together.

You have to push your lungs forward through the drag of the atmosphere. Crushed into your chair — you’re like a leaf in a hurricane. The reason is $$D = 1/2 \rho v^2 S$$. Sixteen times the speed of sound. As you accelerate harder and harder, that light blue Florida sky starts to get darker and darker, and then suddenly, black — and the engines shut off, and you’re weightless.

If the equation $$D = 1/2 \rho v^2 S$$ is for air resistance (drag), then $$S$$ might be $$C_D A$$ where $$C_D$$ is a drag coefficient and $$A$$ is an effective cross-sectional area.

$$S$$ doesn't show up in that Wikipedia article or a few other sites I checked, but is it nonetheless a standard variable or parameter used in spaceflight? If so, what's it called and how is it defined mathematically, and determined experimentally and theoretically?

• S often means wing area. My introductory aero engineering text Introduction to Flight by Anderson gives the drag equation as D = dynamic pressure * S * drag coefficient, where S is the wing area. Not exactly what he shows, though. Maybe he's assuming a drag coefficient of 1.0? – Organic Marble Dec 25 '19 at 14:03

As you correctly noted, the S he's using is a combination of effective surface area and drag coefficient. All literature I've come across uses S for surface area and expresses drag as $$D = C_D\frac{1}{2}\rho V^2S$$ where $$C_D$$ is the drag coefficient and S is the effective surface area.
Combining these two into one parameter makes sense to me however. $$C_D$$ is usually calculated numerically or experimentally and in both cases it depends on your angle of attack. For most shapes, the angle of attack will also have an effect on the effective surface area. The $$C_D S$$ part of the drag equation can therefore be determined as one parameter.
As far as I know, in literature this notation is not used, but it makes sense intuitively to clump them together. The closest I can think of is the ballistic coefficients but that is calculated as $$\frac{M}{C_D S}$$, where M is the mass.