Drag through the speed of sound

Drag is the air holding a rocket back along its path. It grows with the dynamic pressure q, at low speed the pressure the oncoming air would exert if it were brought to rest, which grows with the air’s density and the square of the speed. A simulator turns it into a force with the rocket’s drag coefficient C_D and its reference area A, the body’s cross-section:

q = ½ ρ v²
D = q · C_D · A

with ρ the air’s density and v the airspeed. The drag coefficient is how draggy the shape is, whatever its size; it changes with speed, given here as a Mach number, the airspeed over the speed of sound. It is the sum of three parts:

• Skin friction: the air rubbing along the surface, in the thin boundary layer it drags along. It acts over the whole outside of the rocket, so a longer rocket, or one with bigger fins, has more of it.
• Pressure drag: the air pushing back on every face that meets it: the nose, a shoulder, the fins’ front edges. A smooth, pointed nose has almost none below the speed of sound; a flat fin edge has some at any speed.
• Base drag: the low pressure behind the flat aft end, where the air can’t follow the body round its corner. It pulls back on the base like a suction cup.

HPR Sim builds the coefficient up part by part, following Niskanen’s thesis, which OpenRocket also follows (Aerodynamics). The guides’ rocket, a small rocket for a first certification flight that the repository keeps for its how-to guides (its design file), shows the parts, as HPR Sim computes them: no measurement of this rocket’s drag exists. At Mach 0.3 in sea-level air its drag coefficient is 0.60: skin friction makes 59% of it, the base 22% and the fins’ square edges 19%. Its ogive nose, smooth into the body, adds next to nothing at that speed (report).

A worked example. At Mach 0.5 in sea-level air the guides’ rocket flies at 170 m/s (558 ft/s), so the dynamic pressure is 17.7 kPa. Its reference area is the body’s cross-section, 66 mm (2.60 in) across, and its drag coefficient there is 0.63, so the air holds it back with 38 N, the weight of 3.9 kg.

Air flowing round a nose speeds up, so as a rocket nears the speed of sound the air beside its nose passes it first. Shocks form there, and the pressure pushing back on the nose climbs: the transonic drag rise. Past the speed of sound the nose pushes a shock wave ahead of it, and its pressure drag, now called wave drag, settles to a value set by the nose’s shape and how slender it is. The base’s share of the coefficient grows with speed too, until the speed of sound, and then falls, though the suction itself keeps growing, more slowly. Skin friction’s falls with speed, by a step at the speed of sound in HPR Sim’s rule and faster past it (Aerodynamics has the formulas).

For the guides’ rocket, its drag coefficient climbs to 0.69 by Mach 0.8 and 0.84 at Mach 1, and peaks at 0.88 at Mach 1.07, 45% above its value at Mach 0.3. By Mach 2 it is back down to 0.57. The nose’s pressure drag, next to nothing at Mach 0.5, reaches 0.19 at Mach 1.1. The base’s grows from 0.15 at Mach 0.5 to 0.25 at Mach 1, then falls (report).

Drag grows with the square of the speed as well, so the two compound: doubling the speed makes the dynamic pressure four times larger, and the coefficient is higher besides, so in the same air, at Mach 1 it meets 5.3 times the drag it meets at Mach 0.5. That is why a bigger motor buys less height near the speed of sound than its extra impulse suggests: more of the extra goes into pushing air.

On the faster of its two motors the guides’ rocket reaches Mach 0.84, where the rise has begun: at Mach 0.85, just past that, its drag coefficient is 0.71, 17% above its value at Mach 0.3 (When fins flutter flies it).

Skin friction depends on how rough the surface is. On a smooth surface the friction falls slowly as the rocket gets faster or longer; on a rough one, above a speed that depends on how rough it is, the roughness alone sets it. HPR Sim takes the roughness from each part’s finish, a height in micrometers from Barrowman’s table of surfaces (Aerodynamics).

With every outside part given the same finish, the guides’ rocket’s drag coefficient at Mach 0.3 is: polished, 0.5 µm, 0.49; aircraft paint, 20 µm, HPR Sim’s default, 0.53; the design’s own 60 µm, 0.60; and badly sprayed paint, 200 µm, 0.70 (report). So at Mach 0.3 the drag coefficient is 43% higher with the badly sprayed paint than with the polished finish. The design’s finish is what OpenRocket calls regular paint. Which finish a built rocket has is a judgment: the table describes surfaces, not a hobby rocket’s paint, seams, fillets and decals.

NASA measured the drag of two half-scale models of the Arcas Robin, a sounding rocket with a long nose, thin, sharp swept fins and a short boattail: a short model, the Arcas Robin itself, and a long one with a stretched body. They flew in two wind tunnels from Mach 0.6 to 4.63 (comparison). The models sat on a sting, which disturbs the air behind the base, so the comparison is of the forebody: the drag less the base’s. With its fins on, the model’s measured forebody drag rose from 0.30 at Mach 0.6 to 0.69 at Mach 1, then fell to 0.18 by Mach 4.63: the same rise and fall, on another rocket. The figure sets HPR Sim’s forebody drag against the tunnel’s, on the short model.

Each of the tunnel’s points was read off the reports’ plots to within 0.002 to 0.008 in drag coefficient either way, the band drawn round its dot, most of them smaller than the dot. HPR Sim’s read +12.9% at Mach 0.6, +51.0% at Mach 0.9, the most of the readings below the speed of sound, and +7.1% at Mach 1, the least; then more at every faster speed, to +154.0% at Mach 4.63. At the faster speeds most of that is the fins: HPR Sim gives a fin’s front edge the drag of a rounded edge, which grows with speed, where a thin, sharp fin’s falls. With the fins off, HPR Sim’s read +12.0% to +44.6% high on the short model, and up to +54.2% on the long one, mostly from the boattail, which HPR Sim’s rule over-predicts at these speeds. The models’ finish wasn’t reported; the comparison takes it as polished, a guess, and a rougher one would read higher still. Only 2 of the 44 readings, both models’ with their fins on and off, are within 10%, the target the comparison set before measuring (Aerodynamics has the tables and the causes).

A drag that reads high makes the simulated rocket fly lower and slower than the real one: its apogee, its top speed and its max q, the peak dynamic pressure, all read low. For a flight near a waiver’s ceiling, the height a launch’s airspace permit allows, that is the flattering side: the real rocket may climb higher than the number says. A max q that reads low flatters the fins and the airframe too (When fins flutter). A drag that reads low errs the other way: the rocket flies lower than the number says, the optimistic side for a flier aiming at a target altitude.

The figure marks the flattering side: its thick bars mark each speed where HPR Sim’s drag reads above the tunnel’s. The test a_higher_drag_reads_a_lower_apogee pins what that sign means: the same flight with its drag scaled up reaches a lower apogee, a lower top speed and a lower max q, and scaled down, higher ones, on a rocket that passes the speed of sound and on one that doesn’t. It pins the sign, not how often HPR Sim errs high; the marks show that. On the Arcas Robin, HPR Sim’s forebody drag read high at every speed, so for a rocket of that shape, with thin, sharp fins and a boattail, read its apogee as possibly low.

The tunnel’s rocket is not a hobby rocket, though. On the logged hobby flights of Trusting a simulation, HPR Sim’s apogee averaged +8.73% above the logged one on the 53 flights: on those rockets something leans the other way. Drag that reads low is one candidate; the motor’s thrust and the rocket’s mass are others. No comparison yet sizes HPR Sim’s drag alone on a hobby rocket, so neither direction is a rule for yours.

• The base while the motor burns. HPR Sim takes the burning motor’s cross-section off the base’s area, as Niskanen does; OpenRocket keeps the whole base. No measurement here checks either (power-on drag).
• Drag at an angle of attack. A rocket flying at an angle meets more drag; HPR Sim scales its drag coefficient by a factor of the angle, which no comparison here checks.
• Launch lugs, rail buttons and fillets. The guides’ rocket has none modeled; each adds drag, and HPR Sim models lugs and buttons but not fillets (Aerodynamics).
• The other comparisons. HPR Sim’s drag is also compared with RASAero II’s curves and with a handbook’s worked calculation, neither a measurement (Aerodynamics).

Sources. The tunnel readings are NASA’s, works of the US Government. The logged flights’ weather is ERA5, generated using Copernicus Climate Change Service information 2026, and contains modified Copernicus Climate Change Service information 2026; neither the European Commission nor ECMWF is responsible for any use made of it. The report gives the full attribution and the ERA5 citations.