Aces High Bulletin Board
General Forums => Aircraft and Vehicles => Topic started by: F4UDOA on July 10, 2002, 01:16:58 PM
-
Gents,
I have always questioned the relation of climb versus accleration and I have always been told that they are directly proportionate. When I have argued this relation I have been beaten about the head and shoulders. However what if a test where performed between 4 A/C in both climb and acceleration then the results should be identical right? WRONG!!
In 1989 a group of modern military test pilots known as the "Socioty of Experamental Test Pilots" SETP Web Page (http://www.setp.org/) Perfomed a test called the "End of the Arguement" between the P-51D, F4U-1D, P-47D-40 and F6F-5 to determine which was the best fighter of WW2 using modern evaluation techniques.
The findings are very interesting indeed but the point I will make if this. None of the A/C were even close to being the same finish in climb and acceleration.
Here are the listed weights of each A/C in the test.
P-47D
Weight= 11,535LBS <=3,000lbs light of full combat weight
FG-1D
Weight= 11,000LBS <=1,000LBS light of full combat weight
F6F-5
Weight= 10,681 <==2000LBS light of full combat weight
P-51D= 8,900 <= 1,000LBS light of full combat weight
Climb test to 10,000FT Mil power
1. F6F-5 = 4:15
2. FG-1D = 4:45
3. P-51D = 4:55 <=hard to see exactly on chart
4. P-47D = 5:00
Acceleration Test Mil power at 10,000FT to top speed.
Note: the P-51D started at 120KNOTS. P-47D started at 110KNOTS. The F6F-5 and FG-1D started at 100KNOTS.
1. P-51D<== By a fair margin Top speed attained approx 240knots in 130seconds
2. F6F-5= Top speed attained 210Knots in 110seconds
3. P-47D= Top speed attained 215Knots in 130seconds
4. FG-1D= Top speed attained approx 230Knots in 160 seconds
So none of these a/c finished in the same order in both test.
What gives?
-
The climb = accel thing only applies to instantaneous measurements, not average measurements.
-
Funked,
All the climb and accleration numbers in AH are sustained not instentanious as are these test. I have always said that they are not directly related. I have test data with 4 dissimiler A/C and according to theory they should finish with the same result.
It does not matter what aircraft type was tested. It could have been 4 cessna's. The point being that they should finish in the same order if climb and accleration are tied together.
-
The climb charts on the HTC website are instantaneous rate of climb measured at the airspeed which gives the best sustained rate. AFAIK HTC never published any acceleration figures.
-
F4UDOA, Your taking the word instantious wrong, meens at a single speed for acceleration. I.E. The acceleration from 169 to 170 is different than acceleration from 200 - 201.
Accelerations would be in a unit like Mph change in 1 sec.
Also climb rate at 200 is different than climb rate at 169.
The chart your looking at gives a climb rate at 1 speed, and an average acceleration over different speeds.
When we say Climb rate is always perportional to acceleration we meen that if you have an accelerations of 10 mph per sec and a climb rate of 5000 fps, at 160 mph.
Then if acceleration at 200 mph = 5 mph per sec the climb rate at 200 mph must be 2500.
Note you must hold a constant 200 during climb by either raising or lowering the nose.
And they will always be directly perportional.
HiTech
-
Those climb times look to be from a standing start (only 2000fpm average for a 3000lb underweight P47). So a good portion of that test is not even at the sustained climb speed. I'd expect the F6F to do well from a standing start just because it can get the gear up faster.
As was said, the accelerations were averaged over a range of speeds, rather than at the climb speed. The F6F acceleration might have been the best for the 1st 50mph or so but then dropped off drasticly. Likewise the P51 might have been mediocre at low speeds, but kept pulling strong all the way to 300mph.
-
Perfomed a test called the "End of the Arguement" between the P-51D, F4U-1D, P-47D-40 and F6F-5 to determine which was the best fighter of WW2 using modern evaluation techniques.
Easy, Bf109G6! :p
-
rate of climb is proportional to the excess power of your engine.(i don't remember the exact formula)
That is, the power besides that used to overcome drag at a certain speed.
If you think of power as force*velocity, then, at a given speed your excess power would be (thrust-drag)*velocity.
the difference between thrust and drag is what would cause your plane to accelerate, as, according to good old boy Newton, mass*acceleration equals the algebraic sum of the forces.
Therefore, indeed, climb and acceleration are proportional.
-
Gents(and Hitech;) ),
I am a little confused here still. I understand that when you calculate accleration or climb it is always at one speed.
However my arguement has always been that I felt the F4U acclerated to slowly because of it relative power to weight and low parasite drag. What I was told is that becuase of it's high induced drag it slows it terribly. I always felt this hard to believe that induced drag could slow an A/C that had such good power to weight and low Cdo. But the answer is always that if it climbs bad it has to acclerate bad.
However now I have real world test data that shows the A/C that acclerates the best doesn't really climb the best. According to the test data the P-51 should out climb the others by a large margin. But instead it was 3rd behind a F6F and a F4U. And I am willing to bet if that F6F were 500LBS heavier than the F4U instead of 500LBS lighter(1000LBS weight gain) that the F4U would have been #1 in the climb test.
Also a side note on the 2,000FPM cllimb is that the fuel used was not 100/130 as used in wartime on the Radials. It is said to have lost about 4 inches of map on those A/C. Also it mentions that this change did not affect the MAP of the P-51D water cooled engine.
-
F4UDOA: Try think of it this way lets say we have 2 planes plane A with a max speed of 300 PLANE B with a max speed of 350.
The Plane A best climb rate is 4000. Plane B is 3000. Boths best climb speed is 160.
Whos has the best acceleration at 160.
Who has the best acceleration at 300 mph
Who has the best climb rate at 300 mph.
"I understand that when you calculate accleration or climb it is always at one speed."
If you realy understood this you wouldn't be confused by the chart because it is not messuring acceleration at 1 speed. Its messuring acceleration over the entire speed range.
I.E. It's average acceleration. That would be like messuring climb rates at different speeds then taking the average of those rates.
We are realy talking about 2 completly different messurements, your viewing acceleration as time to reach top speed. Im viewing it as a change in speed per sec at any given speed.
If in my example Plane A & B both started at 160 and went full throttle Plane A would first pull head of plane B, i.e. better acceleration, as there speeds increased plane B would catch back up and pass plane A. So early on plane A has better acceleration, later plane B does.
As far as the F4 goes, it accelerates badly at slower speeds as compared to other planes , for the same resones it climbs poorly.
Acceleration and climb are 100% equivilent functions. And it realy comes down to Acceleration = Gravity, gravity is the oposing force in climbing, mass is the oposing force in acceleration.
(I know mass is not a force but for this description it works)
-
DOA,
You need to know the climb speed, which was probably different for each plane? I can guarantee you that the P-51 will outclimb all other planes at 230 knts. The average acceleration to top speed is not indicative of how a plane will accelerate at it's climb speed.
a = Force / mass
RoC = Force * TAS / Weight
Note, that Weight = mass * g
g = gravitational constant (32.2 feet/s^2)
All you have to do to convert a climb rate into an acceleration (at the climb speed), is to mutiply by g and divide by TAS.
A plane that will climb at 50 feet/s, with climb speed of say 220 feet/s, will have an instantaneous acceleration of
50 * 32.2 / 220 = 7.3 feet/s^2
...in level flight. Note, that as soon as speed increases to 221 fps, climb rate and acceleration will both change.
-
Just so I am being clear the acceleration chart is a graph. It shows the acceleration through the speed range.
The P-51D accelerates at a higher rate through out the speed range. Based on this the P-51D should climb quite well through out the speed range. But it finishes third behind the F6F and F4U(which accelerated the poorest).
Having done the testing in AH myself I can say that climb and acceleration are completely linear. This is not so IRL.
So if this relationship is not linear IRL why is it in AH??
-
Wells,
I would expect the P-51D to accelerate faster at 230MPH but it is clearly superior throughout the speed range in the chart. However the climb of the P-51 is clearly inferior to the F6F and F4U.
This is the opposite of what I have been told.
1. I would like Hitech and Wells to get a copy of the 1989 Symposium. It was sent to me free within a week.
2. Is it possibe to calculate a range of acceleration from Vmin to Vmax? It must be because AH's FM's are working examples of this.
My conclusion:
I don't know the math and I probably won't anytime soon. But I want to see someone express a logical reason why a
A. F6F should outclimb or accelerate an F4U?
B. How a P-51D can accelerate better than a F6F but climb worse?
C. Draw a graph of these three things taking place
I have Zigrats performance calculator on my web page here
My homepage(F4UDOA) (http://mywebpages.comcast.net/markw4/)
-
Hitech,
We are crossing post here.
Anyway I'm not reading acceleration as time to read max speed. I know thats how it sounds but I am looking at acceleration at a given speed.
Forgeting about the F4U for a minute and just look at the F6F and P-51. The P-51 has better acceleration througout the range and the F6F has better climb albeit the F6F is climbing at a constant speed. Both A/C are climbed at there best speeds.
The P-51 accelerates faster than the F6F at the F6F's best climb speed. This should not happen, correct?
-
DOA,
I don't have the report to see this chart, but given the info you've provided, the acceleration test is at 10000 ft. The climb performance is measured from the ground up to 10000 ft, right?
These are laws of physics. Those planes are not defying those laws. The only info I can give you, is that at 10000 ft, the climb rate at a given speed will correspond to the acceleration, provided power is the same, etc. Perhaps at lower altitudes, the results are different. Surely, the power will be different at lower heights.
-
Wells,
Everytime I say why does one accellerate better than another I hear "because it climbs better" or why does it climb better? Because it accellerates better. This is not a reason.
Try this.
Forget that we know the climb of any WW2 fighters.
All we know is the weight, wing area, aspect ratio and top speed.
Right off of the HTC webpages
Airplane
#1 F4U-1D
Weight =12,175LBS
Wing Span=41
Wing Area= 314
Aspect ratio= 5.35
HP sea level Mil power= 2,000
#2 P-51D
Weight 9611lbs
Wing span= 37
Wing Area= 233
Aspect ratio= 5.89
HP sea level mil power= 1490
#3 F6F-5
Weight= 12,483lbs
Wing span = 43
Wing area= 334
Aspect Ratio= 5.50
HP at sea level= 2,000
Please show me(anyone) which a/c climb or accelerates the best.
Why?
I have run these numbers through Zigrats spreadsheet about a hundred times and it comes up different than what is generally accepted.
Why?
Why?
Why?
:confused:
-
Start with the basics. What's the absolute 'maximum' climb ability that we can get from a given horsepower? 1 HP is the ability to raise 550 lbs 1 foot in 1 second. So, for your 3 examples, we get:
Corsair:
RoC = 2000 * 550 / 12175 = 90 fps
P-51D:
1490 * 550 / 9611 = 85 fps
F6F-5:
2000 * 550 / 12483 = 88 fps
We know that the planes will never reach those numbers because of drag and reduced thrust with speed.
Now, we look at static thrust. The absolute maximum that we can get from 13' 2" and 11' 2" propellers with the given power is:
F4u and F6f: 9182 lbs
P-51D: 6761 lbs
Of course, you'll never see those kinds of figures due to inefficiencies like drag and other rotational losses, but those apply to all prop planes...
Ok, so now we can look at T/W:
F4u: 0.75
F6f: 0.74
P-51D: 0.70
Now, wing loading and aspect ratio, which will determine lift coefficient for a given speed and thus induced drag. If we square the wing loading, like squaring the lift coefficient, we can get an idea of induced drag coefficients. Multiplying the coefficients by the area gives an idea of the induced drag force for a given airspeed.
F4u: 38.8^2 * 314 / 5.35 = 88356.7
F6f: 37.4^2 * 334 / 5.50 = 84942.9
P-51D: 41.2^2 * 233 / 5.89 = 67148.3
These are not actual drag numbers, but more like index values for comparison purposes. We can say, for example, that the F4u will see 1.3 times more induced drag at a given speed than the P-51D and 4% more than the F6f. Since the F4u has more than 30% greater thrust over the P-51, we can say that the F4u should improve even more over the 51, but the F6f will gain some or maybe even pass the F4u. So, yeah, everything points to the F4u being superior to the 51, but we still don't know parasite drag, skin friction or prop efficiency...anything could happen! Keep in mind that more thrust creates more drag as the propwash goes back over the airframe. That works in the P-51's favour. The P-51 is likely to see a greater benefit from exhaust thrust, due to the higher manifold pressures and RPM that it uses. For a given Cd0, the F4u shows 35% more wing area and drag. If we assume same Cd0, we can say the 51 and f4u will be about the same speed because the f4u has 35% more thrust too.
Wind tunnel tests might help you narrow down the Cd0, while flight tests will then help to get prop efficiency.
-
What i am just wondering about:
Couldnt the differences F4UDOA mentions come from different engine power curves?
I think Wells calculations will be all for SL, right?
And if the test was flown at 10K the relative thrust numbers might differ even more than at SL, cause of different charger gears, prop layouts for different performance characteristics (i.e. P51 for high alt, both F4 and F6 for low to medium alt) and so on.
-
The military power curve of a F4U-1 indeed shows only 2000hp for sealevel, at 3000ft the power dropped already to 1850hp. ("F4U-1 Brake Horsepower VS Altitude" chart oct.44).
The Merlin or Packard engine gains power up to 8000ft or so with miltary power, peaking out at 1590 hp (?)
-
F4UDOA, In your question about why f4u climbs poorly , the primary difference in the f4u is prop effency at best climb rate speeds (lots of HP to small of prop for it).
-
F4U has a "small" prop? I thought Vought slapped an exceptionally large prop to the aircraft requiring either really long landing gear or a bent wing. It has same enging as Hellcat and P47 but the F4U has a smaller prop?
-
Wells,
That is as good an analysis as I have seen. Thankyou. It looks like aspect ratio plays a huge part in determining induced drag.
Hitech,
I agree they could have done a better job with the prop selection from the beggining. However the F6F used the same exact prop blade as the F4U with worse power loading and climbed marginally better depending on which report you read.
Which brings me to my next question.
Aspect ratio is a huge factor in induced drag. The Spitfire used an elliptical wing to offset this. However Niklas posted a document saying that all WW2 fighters has a somewhat elliptical wing and that it didn't make that much difference.
My question is how much difference is there in the wing shape of the P-51, F4U and F6F fro reducing induced drag and what effect does wing taper have??
-
Hi DOA,
An interesting thread, and so many excellent responses! I would have responded sooner, but since you have been receiving almost perfect responses from just about everyone, I haven’t been able to add anything useful until now.
Originally posted by F4UDOA
Aspect ratio is a huge factor in induced drag. The Spitfire used an elliptical wing to offset this. However Niklas posted a document saying that all WW2 fighters has a somewhat elliptical wing and that it didn't make that much difference.
My question is how much difference is there in the wing shape of the P-51, F4U and F6F fro reducing induced drag and what effect does wing taper have??
Firstly, Aspect Ratio is the primary factor in determining the drag due to lift, but the taper or spanwise distribution of area of the wing also has an effect, because if the typically elliptical lift distribution acts upon a wing that has its chord lengths distributed in an elliptical manner, the resulting lift will be distributed almost equally over each square foot along the span. That results in an even and almost constant downwash along the span and thus the smallest amount of trailing vortex, and thus induced drag. For example, a rectangular wing, with a taper ratio of one would result in the same elliptical lift distribution acting on a constant chord length, so that the chords near the tip would be carrying less than their share of the load, while those near the root would be carrying more, which for any given Aspect Ratio results in inefficiency due to the variation in downwash distribution and increased vorticity. For example, a rectangular wing with an AR of 6 would have 5% more induced drag than an elliptical wing of the same AR. At the other extreme, with a taper ratio of zero, that would be a 13% difference. Midway between those two extremes a wing with a taper ratio of 0.5 would have a coefficient of induced drag of only about 1% more than an elliptical wing with the same AR. But it isn’t as simple as that because you can achieve chord lengths that vary elliptically without the traditional symmetrical ellipse shape, and also the elliptical variation in lift can be achieved by twisting the wing, or spanwise variations in the wing section camber. Also the elliptical chord variations we have been discussing are only theoretically true for wings with negligible weight, and has been known to be not strictly true for practical wings since the early thirties. That doesn't answer your question about the specific aircraft mentioned, but it does get you into the right ballpark.
Also I don’t think it has been mentioned yet that the results for the P-51 in the tests you have been referring to are not ideal for comparison because the mustang developed engine problems at 4000ft during the test and had to complete the climb on reduced power. They acknowledge in the report that “the data would not be representative.” That is certainly part of the reason for the disparity along with the problem of averaging the climb rate and acceleration already correctly explained by others.
Lastly, regarding the original question about acceleration and climb, if you are interested in seeing the mathematical relationship between them derived, just ask.
Badboy
-
BadBoy,
I hoped this thread sounded somewhat intelligent. I didn't want to sound like it was whining.
The P-51 did throttle back during the climb but at least it was the same A/C climbing and accelerating. So the relationship should be the same which is what I was questioning. As far as the actual performance goes the Radial engines were all MAP limited by the use of less than ideal fuel while the Merlin was not. Besides the weights of these A/C were all way off, so any results of actual speed or climb are biased by there weights. I think flying characteristics were the focus of their report.
So I understand your point about span distribution what is better?
Higher span loading or lower??
Here are span loadings for several A/C from a Vought report I have.
In no order.
1. F4U-1D======= 294
2. F6F-5======== 291
3. P-47D========345
4. P-51B======== 251
5. P-38J======== 316
Also what is better with taper ratio?? Higher or lower?
From NACA report
1. P-51 Apect Ratio = 5.89 Taper ratio == 2.17
2. F4U-1 Aspect Ratio=5.30 Taper Ratio == 1.47
3. F6F Aspect Ratio=5.50 Taper ratio == 2.00
What does this tell you??
-
Originally posted by F4UDOA
I hoped this thread sounded somewhat intelligent. I didn't want to sound like it was whining.
Certainly not whining, but it looks as though you are heading somewhere with your questions, I’m not sure where, and please forgive me if I’m mistaken, but it doesn’t look to me as though you are simply trying to learn something about aerodynamics, I get the feeling you have a point to make?
The P-51 did throttle back during the climb but at least it was the same A/C climbing and accelerating. So the relationship should be the same which is what I was questioning.
Yep, but there was no mention of engine problems during any of the other tests, so I assume it was running smoothly for all but the climb test, and that might easily account for the difference.
Regarding the data you posted, if I calculate the lift dependant drag due to the trailing vortex wake based on the aspect ratio, the taper ratio, and the sweep angle, using your data supplemented with some of my own, the calculations reveal an induced drag coefficient for the F4U that remains almost constant up to about M0.35 and of the P-51, F6F and F4U, the F4U has the largest coefficient, with just a little less than 2% more induced drag than the P-51 and only marginally more than the F6F. Is that what you were expecting?
Badboy
-
Badboy:
I think his understanding of the relationship between rate of climb and acceleration is confusing him. The question is he believes that the data that he's seen shows that rate of climb and acceleration don't correlate to each other as he has been told.
F4UDOA:
You're asking a complex question which requires a complex answer. You're also misunderstanding the relationship between rate of climb and acceleration. Maybe the following concepts and relationships will help you in understanding the physics and explain the data that you're seeing.
EQUATION FOR RATE OF CLIMB:
Let's start by examining climb performance. For a given aircraft steady state climb is expressed by the following equation:
RoC = (Thrust - Drag) * Velocity / Weight
RATE OF CLIMB IS A FUNCTION OF EXCESS POWER OF AN AIRCRAFT:
To simplify this a little further, since we know Power = Force * Velocity, we can then modify the equation with:
RoC = (PowerAvailable - PowerRequired) / Weight
Where:
PowerAvailable = Thrust * Velocity - (we'll call this Pa)
PowerRequired = Drag * Velocity - (we'll call this Pr)
So in essence rate of climb is deteremined by the EXCESS POWER of an aircraft (difference between Pa and Pr) divided by weight. There is a lot of complexity behind this relationship! Let's explore this further.
PA, PR AND EXCESS POWER VARIES WITH VELOCITY:
Consider the following figure describing the aerodynamic relationship between Pa, Pr and velocity:
(http://www.thetongsweb.com/AH/powercurve1.jpg)
FIGURE 1: POWER-VELOCITY CURVE
Figure 1 describes the relationship (T-D)*V relationship in the RoC equation.
SO HERE ARE THINGS TO NOTE FROM THIS GRAPH:[LIST=1]
- Pa and Pr vary with velocity. Pr specifically is a function of total drag [incidently the u-shaped curve occurs because induced drag is high at low speeds and decreases with velocity while form drag is low at low speeds but increases with velocity].
- For a given velocity (or a given point on the x-axis above) you have a specific excess power (Pa-Pr) value for that velocity. In other words the amount of excess power changes with velocity.
- The best rate of climb occurs at the SPECIFIC velocity where excess power is at it's greatest [ where (Pa-Pr) is at maximum]. In the figure this is noted as Vr/c-max. SO IN OTHER WORDS BEST RATE OF CLIMB IS A FIXED POINT INSTANCE AT A SPECIFIC CONSTANT VELOCITY.
EXCESS POWER (Pa-Pr) = ACCELERATION IN LEVEL FLIGHT:
If an aircraft is not in a climb and in level flight, excess power translates into acceleration for an aircraft. This is how acceleration and an aircraft's rate of climb relate to each other. Excess power governs the rate of climb as well as defines an aircraft's acceleration in level flight. Maximum acceleration for an aircraft will occur at the speed for the best rate of climb of that aircraft. NOTE THAT THIS IS ONLY A POINT INSTANT IN TIME, HENCE THE TERM INSTANTANEOUS ACCELERATION.
2NDLY if you look at figure 1 remember that excess power varies with velocity, therefore as an aircraft accelerates through it's it's envelope of airspeeds THE RATE OF ACCELERATION CHANGES BASED ON CHANGING (Pa-Pr). Looking at figure 1 note how Pa-Pr is small at the left of the graph, then increases as velocity increases until Pa-Pr reaches some maximum value (velocity for best rate of climb) and then decreases as velocity continues to increase until you reach max level speed. This entire acceleration profile is then the AVERAGE ACCELERATION of the aircraft, or the acceleration of the aircraft as it goes from one velocity to another.
Here's one of the places that I think you're getting tripped up at. Best rate of climb = where the rate of acceleration is at the maximum. This is only a point instant in time and can only be described at that SPECIFIC VELOCITY. What you are looking at from the report data is a snapshot of AVERAGE ACCELERATION over range of velocities.[/i]
There's more...
PA-PR VS. VELOCITY CURVES DIFFER FROM AIRCRAFT TO AIRCRAFT:
So now we are at the point where we understand and analyze comparisons of rate of climb and acceleration between different aircraft. The Pa-Pr vs. Velocity curves for each aircraft are a function of their aerodynamic characteristics (as simplified by the RoC = (T-D)*V / W equation). Let's use for the sake of comparison the F6F-5, F4U-1D, and P-51D as already mentioned above. With what Wells has already provided as well as knowing some general things about the aircraft in question we can make some rough calculation to give us some guesses at their power vs. velocity curves look like. Figure 2 is a rough stab at this at SL.
(http://www.thetongsweb.com/AH/powercurve2.jpg)
FIGURE 2: DIFFERING POWER-VELOCITY CURVES
So the reason you are seeing the differences in AVERAGE ACCELERATION snapshots of the aircraft in question is demonstrated by these curves. You can see that at lower speed ranges the F6F probably out accelerates the P-51D (F6F Pa-Pr is greater than the P-51D Pa-Pr). But then at higher speeds ranges, the P-51D out accelerates the F6F because at higher speeds the Pa-Pr for the P-51D is greater than that of the F6F.
Here's another place that I think you're getting tripped up at. Each aircraft has it's unique power-velocity curves based on it's aerodynamics which determines varying rates of climb and rates of acceleration over varying velocity. Rates of climb are not constant but vary with velocity. This means that if Plane A has a better rate of climb vs. Plane B at a given range of velocities (hence better acceleration at those velocities), you cannot assume that Plane A will maintain that rate of climb advantage over (and out accelerate) Plane B at a different range of velocities.[/i]
Hope this helps.
Tango, XO
412th FS Braunco Mustangs
-
@dtango: Little of topic, but can you post a Pr/Pa diagram for the FW190D9? Best with three different powers (1750/1900/2100PS).
-
Naudet:
I'll take a look at it. I'm thinking you want something that is more of an accurate depiction of Pr/Pa curves for the 190D-9. Figure 2 above really is a rough stab and meant for illustrating a concept. To put together accurate Pr/Pa curves, even an accurate estimate is pretty involved. At any rate I'll look into it and see how far I get and post request for info or findings in a new thread.
Tango, XO
412th FS Braunco Mustangs
-
One more thing regarding Aspect Ratio and induced drag, it's a mistake to assume that AR is the primary factor in determining induced drag. Here's why:
It is true that the induced drag coefficient equation is:
CDi = CL^2
-------------------
pi * e * AR
We also know the following as well...
AR = b^2
----------
S
and
CL = 2W
-----------------
S * rho * V^2
and that
Di = CDi * S * rho * V^2
If you substitute the equations for CDi and CL and AR you'll end up with the following equation for Di in level flight..
Di = 2W^2
------------------------
pi * rho *e * V^2 * b^2
So what does this tell us? Something interesting:
(1) From an airframe perspective weight and wingspan (b and not AR) are the major contributors to induced drag. If you want to reduce induced drag, decrease weight or increase wingspan.
quoting Don Stackhouse at DJ Aerotech:
So what controls induced drag? Essentially it's a function of the amount of lift being made (weight and bank angle), how much air is being influenced by the wing (i.e.: "mass flow"), and how efficiently the wing uses that mass flow. Mass flow depends on the density of the air, the speed of the aircraft, and the wingspan. Note that I did NOT say "aspect ratio". Induced drag is NOT directly a function of aspect ratio. For a fixed wing area, an increase in aspect ratio will improve induced drag, but only because the only way to increase aspect ratio for a fixed wing area is by increasing the span. It's SPAN that controls mass flow, NOT aspect ratio and NOT wing area!
(2) Span efficiency (e) is what Badboy was referring to regarding taper etc. Span efficiency is partly a function of AR. Span efficiency is between .7-.9 for most planes. WW2 Aerodynamic changes such as elliptical wings, rounded wing tips etc. etc. still puts span efficiency in the .7-.9 range.
Tango, XO
412th FS Braunco Mustangs
-
Originally posted by dtango
So what does this tell us?
That induced drag doesn't change with altitude... Just kidding, I don't mean to be picky, but you don't have a complete dynamic pressure term because you dropped rho from the denominator of your final expression. Otherwise, well explained.
Badboy
-
Naudet,
Here's what I came up with for a Fw-190D-9. This is based on mass of 4270 kg, 1680 PS at 6600m (1800 PS at sea level), where the plane did 686 km/h. The results are (assuming 20% losses to the propeller efficiency):
Best climb (initial): 17.4 m/s @ 265 km/h ias, reduce climb speed to 250 km/h @ 6600 m (14.3 m/s).
The zero-lift drag coefficient (Cd0) is about 0.022.
First one, thrust and drag curves...
sea level
(http://www.iaw.com/~general6/fw190d-9_thrust_sl.jpg)
6600m
(http://www.iaw.com/~general6/fw190d-9_thrust.jpg)
Then, climb performance vs speed:
sea level
(http://www.iaw.com/~general6/fw190d-9_climb_sl.jpg)
6600m
(http://www.iaw.com/~general6/fw190d-9_climb.jpg)
Finally, glide ratio vs speed:
sea level
(http://www.iaw.com/~general6/fw190d-9_glide_sl.jpg)
6600m
(http://www.iaw.com/~general6/fw190d-9_glide.jpg)
-
D'oh! Thanks for catching that Badboy. Corrected above now.
Wells- I was just about to fire off an email to consult with you on the D-9 graphs :D using your little program.
Tango, XO
412th FS Braunco Mustangs
-
Great curves wells.
But i could need a little explanaton, especailly for the 1st two diagramms, cause i don't know which of the four curves illustrates what. Which colour has the drag curve, which colour is the thrust curve and so on.
The climb curves i understand.
And the glide ration i don't even ever heard off.
Sorry that i am such a aerodynamics novice.
Btw would it help you if you would have a power curve for the JUMO213?
I have one if you want i will attach it here, so you can take exact power outputs for all settings (1700/1900/2100PS).
-
Thrust - drag curves...
White - thrust available
Yellow - induced drag
Blue - parasite drag
Green - total drag (thrust required)
To convert this to Pa / Pr - multiply thrust available by velocity over the range of velocities to get Pa and multiply total drag by velocity to get Pr.
Tango, XO
412th FS Braunco Mustangs
-
Back to the original subject.
Question.
Why would Vought engineers build a wing with so much induced drag? It had the lowest aspect ratio of any of the 5 major American fighter types as well as the lowest taper ratio?
What gives?
-
F4UDOA you are overthinking this. :) I
hihgly doubt Vought cared so much about this as the past 60 years of development and plain time to think or argue about the finer points of aerodynamics have. You could just the same ask why they did not incorporate laminar flow wings, or why they didn't cover the outer wing in metal instead of fabric, or why they went with a bent weng-we know other navy planes with R2800 didnt need them. And so on and so on.
Or one can say they simply were not as smart as the NA enginners who designed the P51 wing, or Kurt tank who designed the very taperd very high aspect ratio Ta152H wing.
But seriously the only logical reason I think it was to maximize wing area while minimizing wingspan.
-
F4UDOA:
I guess you missed my post above on induced drag - see just a couple of posts up.
(1) AR is not the primary factor determining induced drag. Weight and wingspan are.
(2) AR, taper ratio have more to do with span efficiency - e which usually is between .7 - .9. WW2 wing planform improvements to improve span efficiency makes only a minor impact on induced drag.
Tango, XO
412th FS Braunco Mustangs
-
Grunherz,
The F4U was porbably fying before the first Laminar wing was built. Putting a laminar wing on a carrier fighter was probably not anyones thinking in 1939.
What I can't understand is why with some seemingly minor changes to the wing design the F4U could have climbed much better. I realize that everything is a trade off of one feature or the next. I am just trying to understand the why. The P-51 and TA-152 are purpose built and it is easy to see what the designers where thinking at the time. I am trying to get inside the head of Rex Beisel who has been dead a long time. BTW Rex is the guy who put the oil coolers in the wings of the F4U making the cowl opening smaller than the F6F and P-47. This design was copied in the F8F Bearcat. Obviously Rex was the influence behind the Bearcat not the FW190.
Dtango,
I must have really been out to lunch because I completely missed your post. However now that I see the equation for Cdi, I am really confused.
This is why.
The Cl max of the F4U is very low compared with the F6F or any of it's contemporaries. It is 1.49 power on no flaps. The F6F by comparison is closer to 1.8. I am not sure what E represents in your equation but it would seem that the number will be much smaller in the F4U because of the lower Clmax.
-
If you go back to the induced drag equation in level flight you will notice that Cl doesn't factor in. The related variable to Cl in induced drag is the airspeed [edit: and weight]. Cl is really a measure of AoA which is a function of the airspeed and weight of the aircraft.
Clmax is the maximum AoA a wing can obtain before an aircraft stalls. I may have to think through the following statement to make sure it is technically accurate but the F4U having a lower CLmax value just says that it can't generate as much lift at slower velocities vs. other a/c with higher Clmax values. Clmax occurs in level flight at the stall speed of the aircraft.
Clmax isn't related to span efficiency - e.
Tango, XO
412th FS Braunco Mustangs
-
Originally posted by F4UDOA
What I can't understand is why with some seemingly minor changes to the wing design the F4U could have climbed much better.
Because aircraft don’t climb on their wings, they climb on their engines. During a sustained climb, the wings only support a little less than the weight of the aircraft, the climbing is done by the engine’s excess power. The more excess power, the higher the rate of climb, the more excess thrust, the steeper the climb. That’s slightly simplistic because of course the excess power is partly determined by drag and thus by the wing, but even so, a designer trying to increase the climb rate would be more likely to look towards the engine and propeller combination for improvements. For example, when paddle blades were retrofitted to aircraft during WWII, their higher activity factors meant that much more of the engines power could be absorbed and pilots noticed a very dramatic increase in climb rate.
The Cl max of the F4U is very low compared with the F6F or any of it's contemporaries. It is 1.49 power on no flaps. The F6F by comparison is closer to 1.8. I am not sure what E represents in your equation but it would seem that the number will be much smaller in the F4U because of the lower Clmax.
The number normally represented by the character e in induced drag calculations was originally known as Oswald’s efficiency factor, and his original paper is available for download from the NACA report server. More commonly it has a component of parasite drag lumped in with it and is just called the airplane efficiency factor and can be estimated depending on the aspect ratio, taper ratio, and sweep angle. Theoretically the Spitfire would have an efficiency factor close to 1, meaning that it will have a coefficient of induced drag close to the theoretical maximum. You might expect most WWII fighters to fall somewhere above 0.8. Aircraft with higher values will produce less induced drag, which is why the Spitfire holds its energy so well in a turn, aircraft with lower values will produce more induced drag so they tend to bleed energy more quickly during turns. The value for the F4U is lower than the Spitfire, but only because its wing shape has a less elliptical lift distribution, not because of the difference in lift coefficient.
The efficiency factor, and the lift coefficient both have an influence on the amount of induced drag when the aircraft is maneuvering, but independently of each other. For example, even if an aircraft has a high efficiency factor, it may still produce more induced drag than one with a lower efficiency factor if it produces more lift. That means that an aircraft may lose energy much more rapidly than another when maneuvering close to their maximum coefficient of lift, and yet lose energy less rapidly when they are both in level flight.
Hope that helps.
Badboy
-
DOA,
There is a really great book put out by AIAA, the Author's last name is Raymer I believe. It's an introductory book to aircraft design.
Many decisions are made when designing an aircraft. It's more or less a balancing act. If you want a certain performance aspect in an aircraft, other parts may suffer, or may not be needed. LIke the wing of the corsair. It affords speed and maneuverability, but may induce more drag, but in the overall scheme of things, that drag may be negligible.
An elliptical wing is the best wing design for a low Cdi (induced drag) coefficient. But, if you do some quick back of the envelope analysis you can approximate that Cdi very closely by using a tapered or sectionally tapered wing. So close in fact, you can argue that the difference is negligable in most cases. Again depending on how you 'optimize' your design. Again, aircraft design is give and take, you change one equasion...and low and behold all the others are changing to reflect it. So you really have to become creative on how you tweak your design and what is truly desirable.
I highly recommend the above mentioned book, it may be pricey but you can get it used pretty reasonably. It's been awhile, my aero is a bit rusty, I haven't done any basics in awhile. But I work on aircraft everyday and it's a great field to have an interest in.
Also for anyone interested, Bruce Bohannon is doing some crazy time to climb record breaking in his Exxon Tiger. Check it out.
NAWC
-
Originally posted by F4UDOA
Back to the original subject.
Question.
Why would Vought engineers build a wing with so much induced drag? It had the lowest aspect ratio of any of the 5 major American fighter types as well as the lowest taper ratio?
What gives?
They probably figured that they needed a certain wing area to get the takeoff and landing speed/distances they wanted. Then the span had to be such to fit into carrier elevators and hangers and things. Vought chose to fold the wings up instead of back, like on the F6f.
-
Great explanation Badboy.
On a tangent Badboy is hitting a principle to keep in mind when he mentions that e and Cl have independent impact on induced drag while an aircraft is MANEUVERING. This is a different state vs. "level-flight" or "constant velocity climb".
The principle is- aerodynamics is the field of dynamics meaning you have to be mindful about the various states or parameters of flight you are analyzing because they change depending on the state of flight. Things are tricky indeed.
For instance back to Clmax, Clmax occurs at a specific condition- in the case of level flight at the stall speed of the aircraft which occur at different velocities for different airframes. Comparing Clmax values doesn't make sense unless you are comparing the Cl values at the same velocity.
Tango, XO
412th FS Braunco Mustangs
-
Actually it was a copied off the commie Yaks. IIRC the Bearcat doesnt actually have the oilcoolers in the wings, it just has the air intakes for them there, unlike all the Corsairs except AU1 who actually have the coolers in the wingroot. :p
Why were the outer wings covered in fabric untill the -5?
-
Grunherz,
Most fighters had fabric covered control surfaces to the bitter end. The P-51D had them until the D-15 I think it was. The F6F, Spit and many others. Why fabric? Why not I guess. I have no idea.
Gents,
I do really appreciate all of the explanations. The bizarre thing about them however is the ambiguity of terms.
BadBoy mentions that an A/C climbs on it's engine(If this is true the F4U-1 should climb with the best American A/C). So this would lead me to believe that power loading is the key to climb. Wrong====>Wells says that aspect ratio is the key to climb. Wrong====>Dtango says the Cli is the ticket but wait, you can't really measure it unless you know what speed the climb is taking place and the AoA. I'm sorry about the sarcasm but it seems like one big circle.
I was almost satisfied with Wells answer of an index # with A/R being the determining factor. But then seeing the equation for Cli makes me believe otherwise. However without knowing Oswalds number I may never know the answer. Is Oswalds number engineer code for an unexplainable situation? Like a boondoggle?
Frankly I'm begging to believe that the way engineers really find out how an A/C fly's is say "Hey Tony, go take the one at the end of the line" and then make up equations to explain the results.
BTW, Spanloading. I listed some numbers for spanloadings of several A/C. How do I interpret these numbers. What is optimal?
1. F4U-1D======= 294
2. F6F-5======== 291
3. P-47D========345
4. P-51B======== 251
5. P-38J======== 316
-
F4UDOA:
I think you're missing it. Badboy, myself, and Wells have all been saying the same things.
#1 The aircraft with the highest EXCESS POWER / weight has the best rate of climb. This is what I've said. This is what Badboy has said. This is what wells has said before in other posts. The nuances that you are missing are that:
(a)Engine BHP ISN'T A MEASURE OF EXCESS POWER. It's more complicated than that. Try and read through my post up above that I did with all the Pa/Pr graphs etc. to try and explain.
(b)Best rate of climb OCCURS AT A SPECIFIC VELOCITY for an aircraft. THIS VELOCITY DIFFERS FROM AIRCRAFT TO AIRCRAFT and you have to be careful when you compare BEST rate of climb between aircraft. E.g. Plane A, Plane B, Plane C are being compared. Plane A has the best rate of climb between all 3 aircraft. What that means is Plane A's BEST rate of climb is higher than Plane B and Plane C's BEST rates of climb. That doesn't mean that at a different velocity Plane A climbs better than Plane B and Plane C, infact it might not at all.
#2 Wells is trying to point out the complexities in statement #1 that engine BHP isn't the measure of excess power. It is a complex relationship simplified by the express (T-D)*V/W. He's trying to point out as I was trying to point out in my Pa/Pr curves that excess thrust changes with velocity as thrust, induced drag and parasite drag changes with velocity. Specifically he's trying to address the specific question you had related to how induced drag factors into the equation and that the F4U has a higher induced drag vs. the F6F and P-51D.
#3 My statements about Cl was directly related to specifics of analyzing induced drag as we were running down the rabbit hole regarding Clmax figures which is Clmax figures doesn't mean squat as it is relates to comparing induced drag between aircraft when analyzing BEST rate of climb.
Tango, XO
412th FS Braunco Mustangs
-
yeah, we're going around in circles here. Now DOA is talking about optimization...
Look at the thrust/drag curves again. See where the 2 drag curves cross each other? That's the lowest drag and Cdi happens to be exactly the same as Cd0 at that point. The best climb performance is not far from that point. It's at a little faster speed, but for all intends and purposes, it's close enough! So, you're given an engine and you're told, "Make a plane that climbs good!" So, you slap a propeller on the front and you build something that is as light and streamlined as possible. However, we need to be able to takeoff in 500 ft, so we determine that we will need a wing area of 314 sq ft for our estimated weight of 12000 lbs! Forget about induced drag for a second...
Using
roc = (T - D) * V/W (that's not a Volkswagon)
We can find our 'optimum' climb speed. We can't possibly make it any lighter and we can't possibly make it any more streamlined and we can't possibly get more power out of the engine. This is the best we can do!!! But, we still haven't chosen an aspect ratio for our wing yet! But, now that we've drawn our graph to find out what the best climb speed is, we're in business! All we have to do is choose an aspect ratio that will give us Cdi = Cd0 at our best climb speed! Ta-da!
I just ran some numbers for the F4u-1. Best climb speed = 66 m/s (148 mph). Cd0 ~ 0.0167. To give a Cdi = 0.0167 @ 66 m/s, we'd need an aspect ratio of about 9. The f4u probably loses a potential 200 fpm by having a lower aspect ratio. Is that really worth losing 30% in roll rate?
-
For Anyone interested there is another great book on the development and test of the F4U Corsair titled "Whispering Death" It's written by one of the actual test pilots, I can't for the life of me remember his name.. But check it out, might be able to find it on Amazon.
Nawc
-
btw: is wingarea the projected area (looking from above) or the "true" wingarea.
Because the inverted gull wing of the F4U reduced effective wingarea imo a bit, especially the inner part has a ~30° angle down looking at it from straight forward, so effective wingare is lower.
niklas
-
Originally posted by Nawc
For Anyone interested there is another great book on the development and test of the F4U Corsair titled "Whispering Death" It's written by one of the actual test pilots, I can't for the life of me remember his name.. But check it out, might be able to find it on Amazon.
Nawc
I have been under impression that it was the Beaufighter which was called "Whispering Death" due to it's quiet sleeve valve engines. I think the F4U was called "Whistling dead" due to whistling sound from oil cooler intakes.
gripen
edited: Oops I mean "Whistling death" ;)
-
F4UDOA
Most of the entire outer wing panels on all WW2 F4Us were covered in fabric. Not just control surfaces, in fact the ailerons were metal in Corsairs IIRC.
So why? :)
-
Gripen,
You are indeed correct, and I did mean Whistling, just a brain fart I guess. I'm embarrased since my grandfather used to build Corsairs for chance vought during ww2 in Bridgeport Conneticut. He's told me many stories. He has some nice cockpit instrumentation to go along with them too. Leftovers after the war I guess.
The book is titled: "Whistling Death" by Boone T. Guyton who was a test pilot on the program. It was pretty interesting reading, not exactly a page turner, but filled with the little quirks about the aircraft and some interesting stories about some crash landings, and performance. Great book for any aviation-historian.
Thanks for the catch Gripen.
Nawc
-
Nawc,
Hehe, I new you would get that title right eventually.
I have Whistling Death as well as "I flew them first" by Don Armstrong who was the lead test pilot for Goodyear on the F2G. Also I believe the other book you mentioned "The fundamentals of Fighters design" by Ray Whitford(sp).
Frankly Wells hit the nail on the head when he said that Vought was trying to meet specs and at the end you have to choose between induced drag and roll rate. I would take the roll too. I just like to get inside the engineers heads that built these things. Not the cookie cutter government funded stuff that gets built today. I would luv to talk to Steve Hinton who won at Reno in 1985 with a F4U-1 with a R4300 on it. He did some wing modifications to lower the drag.
Grunherz,
I get the feeling your going somewhere with this. What is the answer?? I can tell you that most WW2 A/C were a combination of fabric and stressed metal. What do you think?
-
DOA,
The other book I was refering too is a current day guide to Introductory Aircraft Design, published by the AIAA and authored by Raymer, sorry can't remember his first name. This book takes you through the whole design process as it should occur. So you get a great perspective on how design decisions are made. If you really want to get into it, get a program such as mathcad or tksolver and run all the equations yourself and you can see all the relations. I used this book as a bible for my first aircraft design project for my Senior project in college. I used the 4th edition I believe.
Take a look, you can probably find it on AIAA's web site. Actually I just looked it up it's called "Aircraft Design a Conceptual Approach" I know, I don't have a good average on titles today. By Daniel Raymer. http://www.aiaa.org/store/storeproductdetail.cfm?id=529
Have fun,
Nawc
-
DOA you should come to the airshow at Chino next year. During the show Steve is quite busy flying several planes, but at the end of the day they open up the flight line and he is very friendly and willing to answer questions.
-
Nowhere in particular F4UDOA. I'm just saying that all sorts of planes have odd or non standard buliding and design decisions. Like fabric covered outer wings of F4U, or its very broad low aspect ratio wing.
-
Constants are for English units, not SI
Rate of Climb = 60 x V x Angle of Climb (in radians)
Angle of Climb = [550 X Prop Eff x sq rt of (Airdensity / 2)]
all divided by {Gross WT/ Power} x sq rt of {GWT/ Wing Area}
inhale
then subract total aircraft drag coeff and subtract 1 / { pi x AR }
AR = wing aspect ratio....
so by equating climb to hp, you only neglect aspect ratio, prop effeciency, air density, gross weight, wing area, and overall drag.
otherwise, it is a perfect ratio.
Accelleration related only to the balance / imbalance of thrust vs drag, and the mass (inertia) of the aircraft F=MA.... A = F / M
As for Wing design, the F4U was originally planned as a straight winged aircraft, but after some of the design had been finished, they decided to install a larger engine. This required a larger prop diameter, and they bent the wings down so that the landing gear would not be long and weak for carrier crashes (landings)
All design is a compromise among competing factors.