Part 2Rehashing Part 1 simple P/W to predict zoom climb is unreliable because it’s a simplification that ignores key variables and their rates of change in flight. Similar issues apply to using max level speed as a proxy for relative drag differences and trying to spread that out like peanut butter across the flight envelope. It’s not appropriate because drag also changes.
If you leave with nothing else from this thread it’s this: Aerodynamics is complex. Using simplifications without understanding the assumptions for them and when they apply likely lead to erroneous conclusions. As an aero Phd once told me “in aerodynamics you can’t avoid the maths”.
This is particularly true for a zoom climb.
Trying to break zoom climb performance to a primary variable is incoherent. Zoom climb is an interaction of many variables all at once and how they change. It’s appropriate to isolate a variable to understand the implication & influence but trying to reduce zoom climb to a single variable or simple figure of merit doesn’t make much sense. Because it’s a dynamic problem we can’t “avoid the maths”. I don’t know of a better way to predict zoom climb but to use an iterative numerical solution to do so.
There are other key aero concepts we could address. There’s some cool stuff we could break down in terms of details of zoom climb performance too. But we’ll cut to the chase since there’s so much angst with the B-239. For those interested there’s another exhaustive thread done in the past that covers zoom climbs in a fair amount of detail here:
http://bbs.hitechcreations.com/smf/index.php/topic,266321.msg3328531.html#msg3328531Zoom Climb Results: Tango’s Model:So what do the numerical solutions tell us about zoom climb of the B-239? There are at least three indicators of zoom climb performance we could look at:
1) zoom climb height,
2) zoom “hang-time” (as Bozon has pointed out already),
3) rate of energy change
To keep things simple we’ll just look at zoom climb height for the B-239, A6M5b, & P-47D-40.
B-239: BHP=1000hp, S=208ft^2, Prop Diam=9ft, CD0=.028, Weight=4857lbs
A6M5b: BHP=1100hp, S=229ft^2, Prop Diam=10ft, CD0=.023, Weight=5321lbs
P-47D-40: BHP=2600hp, S=300ft^2, Prop Diam=13ft, CD0=.021, Weight=14250lbs
I reset the weights for the B-239 & A6M5b equal AH 25% load out. Assuming a pure 90 degree vertical zoom climb, 360mph initial velocity, 100 ft starting altitude, & airplanes zooming until mph=0 this is what my model predicts:
B-239: 5100 ft in 24.5s
A6M5b: 5300 ft in 25.7s
P-47D-40: 5400 ft in 23.3s
The B-239 technically doesn’t zoom as high but as we can see by the height reached it doesn’t really matter. As we see the greatest gap is a mere 300 feet between the B-239 and the P-47D-40 which in our AH world would be a separation of D 100 only, pretty much a point blank firing solution for the B-239 to shoot the tail feathers off the Jug.
Anyone surprised by the result? I’m sure you would be if you had a perception about the Brewster that doesn’t match real world physics. And that’s the point. What is our basis for perceptions of how a plane should perform? Is it anecdotes, imaginary / erroneous physics, or real world physics? Usually anecdotes trump physics for a lot folks which is completely exasperating. Worse though are folks that will argue based on flawed physics because the math is all there to test their hypothesis for themselves. “In aero, you can’t avoid the maths.”
AH Flight Test ComparisonsSo how does AH compare to my predictions. I tested the B-239 and A6M5b at 25% load using BnZs test approach: dive from a higher altitude to near sea level, stay wings level until airspeed was at 375mph (IAS from E6B), pull up into a vertical zoom climb as near 90 degrees as possible.
A couple of notes: A) On the procedure, trying to do a constant G pull-up at 3g’s per BnZs technique was nearly impossible for me. The pull-up phase will impose a heavy induced drag penalty and worse for the heavier plane. This will fluctuate based on the g-loading which for me was hard to keep constant. B) I totally ignore the pull-up phase in my projections because the math modeling behind that is even more complicated than the integral math used for just a zoom climb.
Nevertheless these are the average results after making many attempts:
A6M5b: 5.05K, 25s
B-239: 4.85K, 23s
First, they don’t match BnZs results. 2nd despite some of the variability that the pull-up might have on the outcome the results are remarkably close qualitatively to what I calculated: The separation between the aircraft is ~200 ft & the zoom time is in the same ballpark of my predictions.
So why is there a discrepancy of about 250 ft between my calculations and the AH flight tests (and a slight difference in time?). This could almost be a meaningless thought exercise because the variability of pull up and actual initial speed at 90 degrees nose up is enough to throw it off, a very real possibility.
An even more intriguing possibility is the fidelity of the flight models. There are a variety of things I have not modeled because it would take me long hours to do so which AH does model. One is aircraft stability. I totally ignore that and assume that all my airplanes can reach 0 mph at peak of the zoom. In AH that is factored in and it is difficult to keep the airplane pointed nose up 90 degrees when airspeed gets low without some heavy control input and you may not actually top out at 0 mph but between 10-40 mph because of departed flight.
Second, AH also models engine HP variation with altitude and RAM air. Engine BHP output can vary as per the way they were designed. For my favorite airplane, the P-51D the Packard V-1650-7 Merlin has a saw tooth BHP range over the altitude range with it increasing from sea level to critical alt, then decreasing, then increasing etc. The point is that engine max power output isn’t a fixed value but varies with altitude and each engine has its own unique “curve”. AH models this. My model assumed a fixed BHP for all altitudes because modeling the propulsion system would require much more detailed data then I have available as well as a lot more time and sophistication to do so.
Here are the AH ROC graphs for the B-239 compared against the P-51D and the A6M5b. As you can see the P-51D has an increasing ROC with altitude to about 10,000 ft. This matches the data I have on the V-1650-7 hp variation. Note for the B-239 ROC remains constant to almost 4000 ft and then drops off indicating that the Wright 1820-G5 outputs a constant BHP until about 4k. Looking at the A6M5b you’ll notice that ROC is decreasing with alt from SL to 8K which means engine power output is dropping off.
So the 250 ft lower difference between my predictions and the AH results is also a likely result of the detailed engine modeling in AH since both the B-239 & A6M5b power drops off.
The point is of course HTC takes their modeling of real world physics and aircraft very, very seriously. The fidelity is incredibly high. Maybe this will encourage others who have an FM dispute in the future to take the time and effort to seriously test their hypothesis before they bring an FM dispute in here because I dare say that 98% of the time HTC has got it right.
