Drag Divergence Mach Number
Estimate the Mach number where transonic wave drag takes off, from critical Mach or Korn's sweep/thickness relation.
Your recent runs (stored only in your browser)
No calculations yet — results land here so you can compare runs.
The engineering
Drag divergence Mach number M_dd marks where transonic wave drag rises sharply — the classic definition is where dC_d/dM = 0.1. It sits a bit above the critical Mach M_cr, the point where flow somewhere on the airfoil first goes sonic. Designers use M_dd to set cruise Mach with margin below the drag rise.
The Korn equation folds airfoil technology (κ ≈ 0.87 for a 1960s NACA 6-series, ≈0.95 for a modern supercritical section), thickness, lift, and sweep into one estimate. Sweep is the big lever: cosΛ appears three times, so raising sweep pushes M_dd up and is why swept wings cruise faster.
Sanity check: with κ=0.87, t/c=0.12, Cl=0.5, zero sweep you get M_dd≈0.68 — right where an unswept thick airfoil starts to hurt. If the number lands above 1.0 with modest sweep, re-check your inputs.
Where this math comes from
Through the 1940s the 'sound barrier' was a real design wall — control loss and buffet from shock-induced separation destroyed aircraft as they approached Mach 1. The critical and drag-divergence Mach numbers gave engineers a way to quantify how close they were before the shocks formed, rather than finding out in a dive.
Richard Whitcomb's supercritical airfoil work at NACA/NASA in the 1960s reshaped the pressure distribution to delay the shock, raising M_dd for a given thickness. The compact Korn relation — popularized in Mason's transonic notes and reproduced in Anderson's textbooks — became the back-of-envelope tool for estimating that number from geometry.
- 1935Volta Congress / Adolf BusemannIntroduces wing sweep as a means to delay compressibility drag rise.
- 1947Bell XS-1 teamFlight past Mach 1 confirms the drag rise is a peak, not a wall.
- 1967Richard WhitcombSupercritical airfoil raises drag divergence Mach for a given thickness.
- 1990W. H. Mason / J. D. AndersonKorn equation form standardized in transonic design texts.
See the full timeline of the math behind every calculator →
Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.