The Meredith Effect-Fact or Fiction?

The success of the P-51 in WW-II is legendary. The underslung, ventral radiator scoop is probably its most recognizable feature, and most pilots have heard the stories about how efficient that radiator system is-perhaps even producing thrust under some conditions.

Back in WW-I, designers of aircraft with liquid-cooled engines didn’t pay much attention to ducting radiators. The radiator began to present a more sizable drag penalty as speeds slowly worked upwards in the mid-1920s. Designers knew the basics by this point: Mass x momentum loss = cooling drag. So, how could mass flow be reduced while still cooling the engine, and how could they reduce the momentum loss of the cooling air? The Schneider Cup racers mainly adopted surface conduction cooling (flowing coolant by the aircraft skin) starting in 1925 with the winning Curtiss R3C. The surface conduction layout was impractical for warplanes and civilian aircraft, however, being vulnerable, heavy, and complicated, so a better solution was sought.

RV-6A balsa core rad scoop showing top profile shape and radiator.

While others may have been contemplating improved radiator designs, it was British scientist F.W. Meredith who first theorized on paper and showed mathematically that it should be possible to not only offset most of the drag of a radiator installation, but possibly produce some thrust by shaping the duct properly and utilizing the added energy of the cooling air exit stream through an adjustable nozzle. His paper was published on August 14, 1935, and much later, his theory became known as “The Meredith Effect.”

The paper used some simplifications and assumptions, which we know not to be valid today, but the report garnered interest on both sides of the Atlantic. In Germany, B. Gothert generated a paper on aircraft radiators dated September 10, 1938. His work was from practical wind tunnel experiments with both hot and cold radiators, and heated simulation grids. Meredith’s theories were mostly validated by Gothert’s actual measurements.

While both papers discussed virtually every consideration imaginable with regards to drag, viscosity, separation, heat transfer, and wakes, they seemed more interested in developing equations to explain every facet of the physics, rather than building and testing actual radiator duct designs which could be used on real aircraft. That being said, these men were both math guys first, and their work was leading edge at the time.

Finished scoop shown inverted, after glassing and painting, minus exit door.

Early Examples

Designers in England took heed of Meredith’s ideas, and ducted radiators appeared soon after on the new Hawker Hurricane and Supermarine Spitfire. Wing-mounted, ducted rads also replaced the original under-engine rad on the BF109 in late 1938, perhaps due to Gothert’s work earlier that year. All these designs had moveable exit doors to control mass flow and cut drag.

The Spitfire and BF109 designers seem to not have had a good understanding of duct dynamics, however, and both suffered from inlet air separation due to the obtuse angles the air was forced to turn between the inlet and rad face, a consequence of having very short ducts. The BF109E duct design gave way to a more complicated design on the F models, having an internal “boundary layer” bleed, movable inlet lip, and double-split exit flaps at the trailing edge of the wing. The G model discarded the bleed, probably because it couldn’t have worked properly due to separation well prior to the rad. Meredith had already noted that efficiency of the rad would be compromised, along with added drag, if inlet separation occurred. The designers seem more concerned with reducing rad frontal area than making sure separation didn’t occur. Despite this, both designs managed to get by in the deserts of North Africa and other hot climates, and both performed well for the times, offering a 100+ mph leap in speed over the biplanes they replaced.

The BF109 and Spitfire rad duct designs couldn’t have produced cooling thrust though due to their inefficient inlet and diffuser designs. Most of the drag reduction on the majority of WW-II fighter designs was simply due to the rad exit doors, which lowered mass flow through the rads in cruise and high-speed flight.

Wing leading edge intakes with buried rads were developed on aircraft like the Westland Whirlwind and Mosquito in the 1938-1940 era. These presented no additional frontal area, but didn’t have very favorable exit geometry and used rather restrictive core designs. Still, these showed lower drag than under-cowl designs when fitted to aircraft like the Hawker Tempest.

Another innovative design of the time worthy of mention is the French Bugatti 100P racer, which was being designed to break world speed records. Their approach was different in that the radiators were totally submerged in the rear fuselage, and air was taken from inlets on the V-tail leading edges, forward through exotic ductwork, then turning to exit from fixed louvers in the wingroots. The designers, however, failed to understand the momentum loss resulting from turning the cooling air 360 degrees through the long ductwork, and the significance of having a variable area exit and the exit smaller than the inlet. This design was finalized around September 1937.

The most uncompromised and functional layout was probably on the British Napier-Heston T.5 race plane, also designed to take the world speed record. Design work was begun in mid 1938. Much of the cooling system layout was done by ducting/cooling expert Arthur Hagg, an ex-deHavilland engineer. The T.5 featured a mid-fuselage-mounted ventral radiator scoop with boundary layer scupper. The exit ducting ran the entire length of the aft fuselage to dump on either side of the rudder, just below the stab. This layout gave the length to construct an ideally shaped diffuser and nozzle for the least losses and drag of any design before or since. The T.5 had all the right stuff to break the speed records-diminutive size, huge hp, ejector exhaust, laminar type airfoil, ultra-smooth finish, and low-drag cooling system. Unfortunately, it overheated on the initial test flight in June 1940, either due to a leak or undersized radiator and ducting, and was written off in a hard landing.

Pitot, static and temperature probes mounted inside scoop to gather flight data.

Cooling the P-51

In the U.S., Curtiss and North American were watching European fighter design and thinking about putting Meredith’s ideas into use. In 1940, the P-51 designers also prioritized the cooling system to make best use of the Meredith Effect. The NA-73X prototype had movable inlet and exit doors on the rad scoop. Eventually, a revised, fixed inlet was used with a boundary layer bleed, based on wind tunnel testing of a full-scale P-51, minus outer wing panels. This was to determine a cause and fix for inlet separation in the rad scoop, which was accompanied by a serious, audible rumble. The long duct of the P-51 was a big improvement over the short ducts used on the Spitfire and BF109. It also integrated oil and intercooler functions like the T.5.

Despite the fact that many tests were run by North American with regards to cooling drag, there is still extensive speculation today as to what drag reducing benefits the P-51 actually enjoys due to its design and the Meredith Effect. Some say the P-51 could offset up to 90% of the cooling drag, others variously insist it produced a net thrust of 250-400 pounds. Calculations with wild assumptions abound on the Internet, but I’ve never seen a definitive answer with real flight test data.

Scoop side profile with exit door fully open.

The Quest for Truth

The question has always intrigued me, so when it came time for a major overhaul on my Subaru-powered RV-6A, I was determined to build an efficient ventral radiator scoop like the P-51 to replace my kluged and much-modified initial attempt from 10 years earlier. I wanted to instrument the scoop and take actual in-flight measurements to at least prove if the basic Meredith Effect was real or not, even if I couldn’t test an actual P-51 to settle that age-old debate.

The Radiator

If we look at a modern radiator, most consist of two tanks connected by flat tubes to carry the coolant. The tubes are thin to break the coolant into many small sheets. This increases surface area and thermal gradient. Between the tubes we have very thin fins, which serve to increase surface area even more. Many fins are pierced or louvered to create turbulence, which helps “scrub” the surface for even higher heater dissipation. The cooling air flows between and over all this structure, dissipating heat from the coolant. The modern aluminum radiator is very efficient at dissipating heat per unit volume compared to an air-cooled cylinder. A small radiator like mine (17.6 x 6.75 inches) has a total surface area of over 3200 in2. In the WW-II era, radiators often used a very different honeycomb construction, which presented far more drag than the tube-and-fin types common today.

The radiator can dissipate more heat if the coolant is hotter and the inlet air cooler. This is called delta T, or the difference between the coolant temperature and the inlet air temperature. It’s generally not practical or good for the engine to increase coolant temperature over 230 F, and we can do nothing to control the inlet air temperature on a hot day. We are forced to work within these constraints.

The Duct

The purpose of the duct is to streamline the external flow around the rad as much as possible, slow down the inlet air without separation to recover as much pressure as possible at the rad face, while equally wetting the entire rad area. The flow is then converged with a smaller cross section downstream to gain back exit velocity. We can also incorporate a variable exit door to throttle the mass flow through the rad and increase exit velocity even more. The door allows us to increase flow in the climb and on the ground while decreasing it in cruise. Lower velocity through the tubes and fins equals lower drag.

The RV-6A was never designed for a liquid-cooled engine and even less so for a ventral radiator scoop. The design considerations were numerous, and I often thought I’d never finish what I started.

I was determined to improve on the P-51 design. My design goals were a bit different from North American’s as I needed to have extended ground cooling on a hot day-something the P-51 cannot do. I used a relatively large inlet of 29.5 in2 to accomplish this and placed the rad much further forward, based on CFD analysis. This increases delta P from the prop blast at the inlet during ground idle conditions.

I wanted to have the inlet transition air smoothly to the rad face without separation. The duct would not have the rad tanks exposed to the airstream, as this would cause high drag and turbulence. After experimenting with wool tufts while feeding the inlet with air from two high-capacity centrifugal blowers, it was found that separation was occurring about two-thirds of the way down the diffuser where internal divergence exceeded seven degrees. This was expected from previous experiments. Guide vanes were then installed in the diffuser to smoothly direct the flow into the rad matrix. Apparently the WW-II designers never thought of this simple idea, although the Bugatti 100P did use guide vanes on its inlets.

I have minimal skill at composite work, so it was a time-consuming and painful exercise for me to build the duct from scratch. I used a balsa core, glassed on both sides for strength. Coolant tubes were run outside the diffuser so as not to impinge on smooth airflow to the core. The tanks on the downstream side of the rad were faired into the duct wall to reduce turbulence, and the rad support structure was faired into both the inlet and exit sides, so only the core matrix was touched by the air. Most designs don’t take this type of care. The P-51 and most P-51 replicas don’t have smooth transitions or shapes here, so they will have turbulence in these places.

Scoop exit door fully closed.

Scoop exit door fully open.

Measurement

Aerodynamics is a complex field and some things are notoriously hard to model or calculate-like radiators and ducts for instance. There are so many interconnected considerations and effects that it’s actually much easier to instrument the actual part and go fly it for the most accurate data.

I wanted to measure inlet and outlet pressures, inlet and outlet temperatures of the air and coolant, plus exit-air velocity. I had most of what I needed around the shop from previous projects-temperature sensors, an ASI, and sensitive pressure gauges. I also wanted to take some video of wool tufting to see what the airflow was doing in and around my duct.

Pressure and temperature instrumentation in the cockpit to collect the flight data.

Flight Testing

I love flight testing and learning new things. After extended ground running to validate ground cooling and test the rebuilt engine and other new systems, the next step was to make sure the duct didn’t change the excellent RV flight characteristics. I couldn’t note any changes other than the cooling margin was much better than the previous setup (which had no fewer than four submerged heat exchangers!).

The ground cooling was excellent. I idled for over 45 minutes at +80 F OAT. The coolant temperature didn’t climb further after 30 minutes, just sitting at 195 F.

Next flights gathered initial pressure recovery and pressure delta data. Ram recovery peaked at 84% with the door closed. Other data points showed a maximum rad efficiency of 92%. Video data followed, which uncovered the fact that the door-actuating mechanism was not stiff enough to keep the door fully closed in flight. I revised the system to solve that problem and started to collect momentum data.

One of the big problems, as far as collecting data, was that the engine now ran too cool. I couldn’t get the coolant temperature above 160 F in level flight, even with the door closed. Calculations showed at lower speeds (hotter air exit temperatures), the best I could do for momentum recovery was about 93%. I had to raise the coolant temp to measure what effect that would have, so I blocked off the cabin heater core which doubles as a secondary heat exchanger. This raised the coolant temperature to around 180-185 F. I was quite excited to see the temperature delta at 125 F and a high speed reading on the rad exit ASI. When I ran calculations later on the ground, they showed a maximum of 104.4% at 80 KIAS. The cooling air was exiting faster than the TAS of the aircraft, proving that Meredith was correct 79 years ago. The strongest factor was temperature delta. I could not correlate his theory that the effect would be stronger at higher airspeeds. In fact, the opposite was true according to my data. Higher speeds resulted in lower outlet temperatures, which reduced the expansion effect in the nozzle. Just for interest’s sake, opening the door fully dropped momentum recovery to as low as 59%.

The magic figure to reach velocity parity at the exit was a temperature delta of 120 F. With higher coolant temps, even higher velocities might have been measured. However, Gothert’s data showed a decrease on core drag up to a certain temperature due to reduced air density from heating and, at a certain point, higher drag, when the air expansion within the rad core caused increased turbulence downstream.

I made no attempt to measure the drag of the scoop externally; my only goal was to see if net thrust was possible as Meredith had theorized. The aircraft is around 6-8 knots faster than before, but many external and internal changes were made to other scoops and heat exchangers, so no valid conclusions can be made as far as what parts had what effect. I am happy with the speed increase for whatever the reason though.

What about the P-51?

I’ll speculate that for various reasons, the stock P-51 probably didn’t produce any net thrust, but only flight measurement could ultimately confirm that as fact. The stock radiator is very restrictive due to its design and depth. This would result in a much larger pressure drop compared to the modern rad designs we have today. There is also likely to be inlet separation due to the larger angular change from the inlet to the top of the rad with the relatively short diffuser. On the plus side, it is running higher coolant temperature than I was, which could offset some of these factors.

Race P-51s like Strega use a much longer and shallower scoop with revised exit door geometry and much smaller inlet without the boundary layer scupper. They also probably use a modern rad design. Their speed secrets are kept hidden from view on the tarmac. Strega is in a different speed realm from my RV and uses water spray bars to cool the rad, plus has to fight considerable inlet temperature rise from the high speeds lowering delta T substantially. I’d speculate that Strega enjoys cooling thrust due to these modifications. I’d love to instrument it or any P-51 to see the true story.

Conclusion

My testing shows that with careful design and attention to detail, a properly ducted rad can offset all internal cooling drag. We see most homebuilt aircraft with liquid-cooled engines fitted with some truly awful and inefficient radiator setups. When cooling drag accounts for between 15 and 25% of total airframe drag, you’d think designers would pay more attention to this aspect. Maintaining cooling air momentum is free speed. I hope this article inspires builders to think more about their cooling system designs.