Sizes a radiator buried in a wing or fuselage, with its inlet diffuser and exit nozzle, for the lowest net cooling drag at the design flight condition. Duct drag and thrust follow F. W. Meredith’s momentum and heat-recovery analysis (ARC R&M 1683, 1935). Results update as you type.
Heights and lengths in inches. Air flows left to right.
| Freestream Mach number | – | |
| Freestream dynamic pressure H | – | lbf/ft² |
| Ram temperature rise | – | °F |
| Coolant minus inlet air temperature | – | °F |
| Cooling air temperature rise | – | °F |
| Heat exchanger effectiveness ε | – | |
| Number of transfer units | – | |
| Velocity in the passages | – | ft/s |
| Passage Reynolds number | – | |
| Heat transfer surface area | – | ft² |
| Diffuser total-pressure loss | – | lbf/ft² |
| Core total-pressure loss h | – | lbf/ft² |
| of which friction | – | lbf/ft² |
| of which heating (momentum) | – | lbf/ft² |
| Total pressure behind core ÷ ambient | – | |
| Exit jet velocity | – | ft/s |
| Exit jet velocity ÷ flight speed | – | |
| Exit jet temperature | – | °F |
| Inlet, width × height | – | in |
| Core face, width × height | – | in |
| Exit, width × height | – | in |
| Diffuser area ratio Aface/A1 | – | |
| Exit contraction Aface/Ae | – | |
| Exit converging section | – | in |
| Exit parallel lip | – | in |
| Overall duct length | – | in |
| Freestream capture area | – | in² |
| Loss ratio (h + hE)/H | – | |
| Duct efficiency ηd, eq. 11 | – | |
| Cold drag power F·h(1 + h/4H), eq. 13 | – | HP |
| Heat conversion efficiency ζ, eq. 22 | – | % |
| Power recovered from heat, ζ·Q | – | HP |
| Net drag power, Meredith estimate | – | HP |
| Net drag power, this calculator | – | HP |
| Ram rise (V/100 mph)² °C, eq. 16 | – | °F |
| Engine BHP if jacket heat = 0.46 BHP | – | BHP |
| Net drag power as % of that BHP | – | % |
Same altitude, temperature, coolant temperature and duct. “Fixed exit” keeps the design exit area, so the heat removed changes with speed. “Matched exit” resizes the exit (a cowl flap) to remove exactly the design heat load. Positive force is drag, negative is thrust.
| Fixed exit | Matched exit, same heat removed | |||||||
|---|---|---|---|---|---|---|---|---|
| KTAS | mph | Heat removed, HP | % of design | Face velocity, ft/s | Net drag, lbf | Exit area, in² | Net drag, lbf | Drag power, HP |
The inlet is assumed to sit clear of the boundary layer (a diverter or splitter plate), so the duct swallows freestream air at full total pressure; the heat exchanger adds no wetted area outside the airframe. Ram compression raises the cooling air to the freestream total temperature before it reaches the core, which is Meredith’s section 4.1 effect.
The core is a matrix of straight air passages with the coolant at one mean temperature. Heat transfer uses ε = 1 − e−NTU with Hausen’s developing-laminar Nusselt number below Re 2,300, Gnielinski’s with an entrance correction above 4,000, and a blend between. Friction uses Shah’s apparent friction factor (laminar) or Filonenko’s (turbulent), with the same entrance correction. Core total-pressure loss adds contraction and Borda–Carnot expansion at the passage ends and the momentum loss from heating the stream.
For each depth up to the maximum, the mass flow is whatever carries the heat load at that effectiveness, the face area follows from the face velocity, and the full duct is evaluated; the depth with the lowest net force is kept. Meredith notes (section 6) that minimum power falls near an air temperature rise of 85% of the initial difference, but that weight forces a lower figure in practice, which is what the maximum depth represents.
Net force follows Meredith’s momentum balance, D = ṁ(V − Ve) − (pe − p0)Ae, with the jet expanded from the total pressure and temperature behind the core to ambient pressure. Heat added at a pressure above ambient is partly turned back into jet momentum (eq. 22), which is how a well-designed duct reaches zero drag or net thrust at high speed. The cross-check table applies Meredith’s own closed-form equations to the same flows; his eq. 13 is incompressible and neglects nozzle losses, so expect the two net figures to differ by a few horsepower.
Diffuser length is the length at which walls diverging at the chosen half-angle reach the core face; the exit duct converges at its own half-angle and ends in a parallel lip half the exit height long, so the jet leaves parallel to the external stream as Meredith requires (section 6). Spillage, lip and external fairing drag are not included. Off-design points re-solve the mass flow so the inlet, core and fixed exit are all satisfied together; speeds where even a fully open exit can’t pass enough air are marked as out of reach.
This page was developed by Joe Wilding using AI. Contact me with questions or feedback on X: @joe_wilding