# Aerodynamics of Domes

Update 2018: This post describes aerodynamic estimates that I made in 2005. If I were to redo the anaysis today, I would use the method from more recent projects.

Both airplane wings and domes are curved on top. Should I be concerned with the aerodynamics of domes? It sure would be embarrassing to have the dome fly away or collapse (see ironwolf.dangerousgames.com/burningman99, archived here).

### Wind Speed

Winds at Burning Man can exceed 75 MPH, and so I’d like to know the amount of drag (horizontal force) and lift (vertical force) that a fabric-covered dome will experience at Burning Man. Then I’ll know how many rebar stakes are needed to tie the dome to the ground.

### Drag

Two different fellows (Gourlay and Mez) have done detailed analyses of the drag forces that structures experience from high-speed wind at Burning Man.

Gourlay analyzed the aerodynamics of a 33-ft high geodesic dome (10-m radius) and concluded that such a dome would experience 5,200 pounds of drag in a 45-MPH wind. Redoing his analysis, a 13-ft high dome in an 80-MPH wind experiences 2,600 pounds of drag. (Update 2018: I no longer can find the original analysis, but I found the person, and his web site is linked above.)

Mez analyzed the aerodynamics of a 30-ft high pyramid and concluded that such a pyramid would experience 8,400 pounds of drag in an 80-MPH wind. Redoing his analysis, a pyramid with the same cross-sectional area as a 13-ft high dome experiences 2,100 pounds of drag. Mez goes further and calculates the drag from gusts at 80 MPH using a “momentum transfer” equation. His result is that drag from gusts is no worse than four times the drag of a sustained wind at the same speed, or in this case, 8,400 pounds. (It’s just a coincidence that we see 8,400 again. This isn’t a typographical error.) (Update 2018: I no longer can find the original analysis, but the pyramid mentioned may be the Pyromid project from Burning Man 2003.)

Both of these analyses are worst-case because they do not account for differences between a smooth hemisphere and a leaky fabric-covered geodesic dome.

### Lift

I’ve had difficulty finding references to the lift of a dome. Perhaps that’s why we don’t see dome-shaped airplane wings. But I’d like some kind of estimate, so let’s assume that a dome has as much lift as a wing of the same area.

A Taylorcraft L-2 army trainer has a wing area of 181 sq. ft. and can lift 1,300 pounds at take off. A 13-ft high dome has a floor area of 531 sq. ft. So such a dome, if it were as efficient as the airplane’s wing, would lift 3,800 pounds. The take-off speed of a Taylorcraft L-2 is about 55 MPH, which means that I have an underestimate, but the dome really isn’t a wing, which makes 3,800 pounds an overestimate. So I’ll just assume that the assumptions cancel out and use 3,800 of lift pounds for now. (Realistically, the lift probably isn’t more than the drag!)

Now really, since the dome is covered with 70% shade fabric, there’s no chance of any lift. The pressure difference on either side of the fabric is eliminated when the air on the high-pressure side simply flows through the fabric to the low-pressure side.

### How Many Tent Stakes

The dome has ten vertices at the base. Assume that the frame is stiff enough to distribute the drag over all of vertices. Then each vertex needs to withstand 260 pounds of drag (or 840 if you use the worst-case momentum-transfer estimate). I already know that a piece of rebar in the playa can withstand over 130 pounds of lift because I can lift 130 pounds, but I couldn’t pull a piece of rebar out. I’m certain that the rebar can withstand as much drag as lift. So, if 260 pounds is accurate, then two pieces of rebar per vertex will do.

### Air Density

The density of air at Burning Man is less than that at sea level. Elevation at Burning Man is about 1,200 meters. That gives an air density of 1.091 kg/m3. At sea level, the air density is 1.226 kg/m3. So at Burning Man, the the air density is about 12% lower. All of this means that the lift and drag will be 12% lower than at sea level.