Commentary, further detail and references for What is Aerodynamic Drag and CdA. Each note is addressed by name so it can be cited from anywhere in the Knowledgebase. Working draft, 2026-09-11.
Animation by the NASA Glenn Research Center.
It shows a two-dimensional circular section, not a sphere: flow arrives from the right, fails to stay attached around the back of the body, and sheds vortices alternately from each side. That alternating wake is a Kármán vortex street, and it is the reason a round body's drag is so much higher than its smooth outline suggests — the body is effectively dragging a hole in the air behind it.
Referenced from: Drag
Referenced to frontal area. From ../Variable CdA/ReferenceValues/drag-coefficient-reference.md, which gives 1.1 at the lower end of the speed range and 1.05 at the top.
This is the steadiest number in either figure. A cube's sharp edges fix where the flow separates, so the coefficient cannot move much with speed — the reference file puts the whole-range variation at about 5%. Rounded bodies have no such anchor, which is the subject of Variable CdA.
Referenced from: Cd
Referenced to frontal area, πD²/4, with the convex side facing the flow.
The measurement is Brevoort and Joyner, Aerodynamic Characteristics of Anemometer Cups, NACA Technical Note No. 489, 1934 — held in this folder as sources/NACA-TN-489_Brevoort_Joyner_1934_anemometer_cups.pdf. They put hemispherical cups of 2.03, 4.03 and 6.00 inch diameter on a balance in the model of the full-scale tunnel at Langley and swept them through 0° to 180° of angle of attack. At 180° — the convex back into the wind, our case — their Figure 4 gives Cd ≈ 0.42 to 0.44, and the curves for every speed they tested collapse onto essentially one line. At 0°, the open face into the wind, the same cups give 1.3 to 1.45, which is where the other familiar textbook value comes from.
Corroborated by Hansen, Untersuchung einer offenen und geschlossenen Halbkugel, Göttingen Ergebnisse IV, 1932, who tested both open and closed hemispheres.
What the number does not cover. Every measurement in this lineage is below the drag crisis. Brevoort and Joyner say so plainly: at 180° the value is practically the same as a sphere below the critical Reynolds number, and their tunnel could not go fast enough to look above it. So 0.42 is well founded over the speeds it was measured at, and nobody has published what a hemisphere does above them.
A sphere at comparable speeds sits at 0.45 to 0.50, so the two are the same within the scatter of the sources. What separates them is what happens at higher speeds: a sphere's separation point can jump rearwards and drop it to 0.15, while a hemisphere's sharp rim cannot move. See Variable CdA.
Referenced from: Cd
Referenced to frontal area, so that it can be compared with the other two shapes.
Published section data is referenced to chord, not to frontal area, because that is what matters for a wing. ../Variable CdA/ReferenceValues/drag-coefficient-reference.md gives 0.05 at the low end of the speed range and 0.008 at the high end on that basis. Converting to frontal area means dividing by the thickness ratio, here taken as 12% for a conventional section:
The division direction is worth a second look, because it runs against intuition. Cd is defined so that the force is the same whichever area you reference it to: Cd₁A₁ = Cd₂A₂. Frontal area is the smaller of the two, so the coefficient referenced to it must be larger. The reference file reaches 0.07 independently and draws the same conclusion — a streamlined shape has roughly 1/15 the drag of a cylinder of the same frontal size, not 1/150.
The one assumption is the 12% thickness. A fatter section referenced to its own thickness gives a higher frontal coefficient still.
Referenced from: Cd
0.07 against 0.42 is a ratio of about 1/6.
The advantage is not a fixed property of the shape. At the low end of the speed range the section is also about 0.42, the same as the half-sphere — a streamlined shape has no advantage at all over a blunt one of the same frontal area down there. Streamlining only pays once the boundary layer can stay attached through the pressure recovery, and whether it can is a question about speed and size, not about shape alone.
The older claim that an airfoil has 10% of the drag of a half-sphere came from dividing a chord-referenced 0.04 by a frontal-referenced 0.42. Both numbers were right; they were not on the same basis. See airfoil-drag-value.
Referenced from: Cd
Referenced to frontal area.
No published citation. The range reconstructs from the numbers on the page itself: a CdA of 0.20 to 0.30 m² spread over a frontal area of 0.3 to 0.4 m² gives Cd between 0.6 and 0.8. Those are the figures a Streamlines field test returns, so the value is internally consistent with everything else we publish.
The lower end is a well-positioned rider in time trial equipment; the upper end is an ordinary riding position on the hoods.
Referenced from: A cyclist is a bluff body
Referenced to frontal area, which is the motor industry's own convention, so these figures are directly comparable with the cyclist's.
No published citation. The range covers the real spread: older or boxy shapes near 0.40, ordinary modern cars 0.28 to 0.32, and the best production shapes at 0.25 and below.
Referenced from: A cyclist is a bluff body
This is the number that needs the most care, because the familiar figure for an airliner is 0.02 and that is a different quantity.
Reference area. Aircraft coefficients are referenced to wing area, not frontal area. A narrowbody has roughly 125 m² of wing but only about 12 m² of fuselage cross-section, so the choice of area changes the coefficient by a factor of ten. To sit beside a cyclist and a car, the aircraft has to be put on the same basis as they are — its whole projected frontal area, which is fuselage plus wing thickness plus tail plus nacelles, or roughly 33 to 40 m².
Lift. An aircraft carries its entire weight on its wings and pays a drag penalty for doing so. A cyclist and a car do not. Including that penalty would compare two different things, so the figure here is the zero-lift drag only.
The arithmetic: a zero-lift CD0 of about 0.020 on 125 m² of wing is a drag area of about 2.5 m²; spread over 33 to 40 m² of projected frontal area that gives ≈ 0.07. Including the drag due to lift raises it to about 0.10 to 0.12.
So an airliner is a genuinely slippery shape — but by a factor of about six against a good car, not the factor of fifteen the headline numbers suggest.
Referenced from: A cyclist is a bluff body