Author Topic: Stall Speed Bug?  (Read 5255 times)

Offline dtango

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Stall Speed Bug?
« Reply #60 on: January 28, 2007, 01:50:52 PM »
Thanks for the corrections and the combined equation Badboy.

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Offline Mace2004

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Stall Speed Bug?
« Reply #61 on: January 28, 2007, 03:13:53 PM »
Quote
Originally posted by Brooke
I've completed my study of F4U-1 stall speed in Aces High vs. the stall speeds listed in the F4U-1 pilot's manual for clean, power off; clean, power on; dirty, power off; and dirty, power on.  I find excellent agreement between the manual and Aces High.

I did some math to figure out a technique that would be repeatable, that would allow steady-state measurements (which are much easier to take), and that would allow reasonably easy avoidance of changing g loads on the aircraft.

My results and analysis are posted here:

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/stallSpeedMath.html

If anyone finds errors with my analysis or data, please let me know.  I've checked it a couple of times, but that doesn't mean there aren't errors, and it would be better if the analysis and data stands the test of being looked at by others.

I'll be interested to see if anyone repeats my tests or applies it to aircraft other than the F4U-1.


Brook, I agree with dtango, excellent write-up.  In particular, your description of the differences in the literature is on the nose.  I have also been working on refining the test technique and am now able to come within a few mph of Pyro's numbers.  Changes I've needed to make to do this includes using 100% fuel and tailoring my stick response curves to allow for very precise pitch adjustments at slow speed; however, this has a detremental affect on normal flying.  

Overall, I think what we're butting heads up against the "engineering" answer and the "practical" answer.  An "engineering" answer derived from precise instrumentation and very specific test conditions is required for an understanding of aircraft design and may be the basis for fulfiling the contract but, from a practical standpoint, it is often of little use to the pilot in the cockpit.  I'll talk about what that means at the end.

Many times you'll find "engineering" data in flight handbooks that can never be met by the average pilot flying an average airplane on an average day.  I think it's probably a mix of engineering vs practical information (and occasionally some factually incorrect data) in literature that results in at least some of the confusion.  The differences between calibrated vs indicated lose their subtleties when the pilot can only see indicated and is in no position to apply position error corrections.  Also, errors sometimes make it into publications and are never corrected.  For instance, NATOPS for 40 years has listed the roll-rate of the A-4 Skyhawk as being 720 degrees per second.  That has been taught in flight training the entire time and is even the roll-rate the Blue Angles announcer used to describe the A-4 to audiences during airshows.  The problem is it's wrong and not just a little wrong.  The correct number is 270 degrees per second which is easily demonstrated with a stopwatch.  A simple typo turned 270 into 720 and has remained there to this day.

Based on the numbers provided by Pyro and yourself I believe you've demonstrated that the modeling of the actual stall point is probably pretty accurate.  I think the discussion and data provided by everyone contributing to this thread also demonstrates the difficulties and significant variations resulting from different techniques and, in particular, the use of airspeed as the principal measurement of stall when in fact AOA is the culprit, airspeed is only a secondary indicator.  Variations in loading, variations in environmental conditions and instrument errors shows why the military has switched to AOA and as the principal indicator of stall.  The nice thing about AOA is that it's a constant and, for the same configuration, the wing always stalls at the same AOA regardless of these other factors.  For instance, in the F-14, 18 units AOA, not airspeed, always indicates the point at which rudder becomes your primary roll control rather than lateral stick.  Doesn't matter what your weight, speed or altitude is, it'll always be 18 units.

Regarding your write-up, there are a few things you should look at.  In your description of "Usual Method" you say that accelerating or decelerating along the plane's direction of travel doesn't affect the stall speed as long as you remain level.  Actually, it does and it can be quite significant but not because of instrument lag, it's because of nonsteady state flow effects.  Yes, there are delays in instrument response but if you're deccelerating at a rate that causes significant lag then you aren't going to get good data anyway.  Changes in flow over the wing take some finite time and a rapid deceleration, even if remaining level, affects the stall point because the flow has not stabilized.  Depending on the wing, the difference between approaching stall at -5mph/sec vs -.5mph/sec can be 5 to 10mph in observed stall speed with the faster deceleration equaling a lower stall speed.  That said, Pyro's technique is probably the technique with the absolute smallest deceleration and therefore (at least from an engineering standpoint) the most accurate measurement.

Another area you should take a look at is your discussion of stalls in climbs and "Figure Climb".  It does not include the vertical (i.e., lift) component of thrust.  This can have a very significant affect on the result just as does G and, the greater the thrust the higher the climb angle and the more stall speed will be thrown off.  To take an extreme example, assume the aircraft has a 1 to 1 thrust to weight ratio.  The airplane would be able to park 90 degrees nose-high at O airspeed and never stall.  In another, less extreme example, make a constant speed climb with a 45 degree pitch angle (assuming thrust is coincident to the aircraft centerline) and 1/2 your lift is coming from your engine and only 1/2 from the wing.  The greater the thrust the greater the climb angle and the less useful the results are.

These are the two reasons why I've duplicated Pyro's test condition of 100% fuel.  The greater weight decreases the thrust to weight ratio and makes it easier to conduct the power-on test with minimum vertical thrust component and it makes it easier to control the rate at which you approach stall.  Assuming no (or small) changes in CG the results at higher weights can be extrapolated to the lower weights.  Also, slight excursions in G can be negated by taking the average of multiple runs while the same cannot be said of either pitch angle or high deceleration rates to stall.

All that aside, where does that lead us regarding the AH stall speeds?  We are pretty sure the specific stall speeds are accurate, at least from an engineering perspective, and they can be replicated under very specific, controlled circumstances.  So here's the rub...why can't we duplicate them or even come close in the case of the power-on numbers without this engineering approach?  Remember, when it comes to flight manuals (versus engineering studies) they are attempting to provide numbers which the average pilot in an average plane on an average day can use using the instruments he has in the cockpit (i.e., indicated AS).  If, as we're seeing here the stall speeds are accurate but not achievable except under very exacting conditions the flight manuals would (or should) say so.  One way to take these practical issues into account would be in the determination of recommended approach speeds and acceleration/climb schedules for launch but I have no information on these so don't know if they take into account a higher minimum usable flying speed; however, since they don't mention difficulty in reaching these numbers (or at least nobody has pointed out where they do this) maybe we're asking the wrong question.  Is there something about the way that approach to stall is modeled that is incorrect?  Is this sensitive to specific flight controllers and their setup (I suspect it is to a degree)?  I don't really know the answer at this point but I do know the "effective stall speed" is much higher than the actual speed.

Mace
« Last Edit: January 28, 2007, 03:19:59 PM by Mace2004 »
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Offline Brooke

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« Reply #62 on: January 28, 2007, 05:49:34 PM »
Quote
Originally posted by dtango
Just to make sure I remember this myself, so the key equations are (in conditions for steady state velocities):

(1) cos(theta) = sqrt [ (1-Rate_of_Climb) / Vairspeed]
(2) Vs1g = sqrt(1/cos(theta)) * Vairspeed

Tango, XO
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Thanks, dtango.

Yep, those are the key ones, although as noted by Badboy, the first one should be:

cos(theta) = sqrt[1 - (Rate_of_Climb^2 / Vairspeed^2)]
« Last Edit: January 28, 2007, 05:56:40 PM by Brooke »

Offline Brooke

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Stall Speed Bug?
« Reply #63 on: January 28, 2007, 06:09:56 PM »
Quote
Originally posted by Widewing

A couple of points, if I may...

I noticed that you were using 18" @ 2,400 rpm for power-on stalls.


Thanks, Widewing.

I used 18" and 2400 for the clean, power-on and 23" and 2400 for the dirty, power-on only as that's what the pilot's manual lists as the power settings for its data.

The technique for riding the stall during a steady-state climb works, too, so one could apply it with climb settings of the power to check against sources that list power-on stall speeds at different power settings.

Quote

As for the F6F-5; the Pilot's Manual provides stall speeds far lower than actual test data recorded in Navy test report NA-83/44177, for a weight of 12,420 lb.


Yep -- the F4F pilot's manual is pretty crappy in its quality of data, I think.  Some of the stall-speed data it lists seems like it they might be way off (like the 50-53 knot stall speeds in the text).

Quote

As I stated previously, there are significant differences between the manual, training films, Navy test data and Grumman test data. Thus, establishing exact stall figures for the flight model requires selecting data deemed most reliable.


Indeed.

Quote

I'm satisfied that the most significant contributor to generating variances in stall speeds is the result of increasing or varying climb angle.


I agree, too.  That's why I like the method of a steady-state climb or descent, riding the stall.  In that situation, nothing is varying other than a gradual change (very gradual) in altitude -- climb rate is steady, g's are steady at 1 g, airspeed is steady, angle of attack is steady, etc.

All that remains then is to correct the stall speed one is riding to level-flight conditions (and to correct for calibrated airspeed of the literature and make the aircraft weights match).

Thanks, Widewing, for the comments and info.

Offline Brooke

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« Reply #64 on: January 28, 2007, 06:11:40 PM »
Quote
Originally posted by Badboy
Hi Brooke


Just found a couple of notational errors:
Badboy


Thanks, Badboy.  I'll get on them and post an update today.

Offline Widewing

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« Reply #65 on: January 28, 2007, 06:23:36 PM »
Quote
Originally posted by Widewing
For which numbers?
 


I've been fighting the flu all weekend and my concentration hasn't been up to par.

To answer Hitech's question; stall speeds defined in the manuals are almost certainly not corrected for positional error. I did not apply any correction, but simply converted knots to mph (F6F) or verbatim from the manual (P-38).

My regards,

Widewing
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Offline Brooke

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« Reply #66 on: January 28, 2007, 06:34:16 PM »
Quote
Originally posted by Mace2004

Regarding your write-up, there are a few things you should look at.


Thanks, Mace.   Good points and comments.  I'll correct the description of significance of horizontal acceleration.

Quote

Another area you should take a look at is your discussion of stalls in climbs and "Figure Climb".  It does not include the vertical (i.e., lift) component of thrust.  


Figure Climb is mapping everything to the airplane's coordinate system, where lift is perpendicular to velocity vector.  In that coordinate system, thrust is along the velocity vector (well, there is sin(alpha) of it in the lift direction, but that is negligible for WWII aircraft), and drag in that coordinate system is opposite the velocity vector.

So, thrust does not matter in the calculation.  Angle of climb does matter, but that is taken into account.  All that matters is that everything is steady state, and then the equations correct everything back to what the level-flight stall speed is.

In your example of thrust-to-weight of 1:1, for full power on, v_stall is 0 mph (i.e., there is no stall) -- the aircraft isn't going to stall -- so that is correct.  For T:W such that climb angle is 45 degrees, in the coordinate system of the plane, there is no lift component that is from thrust.  The weight, though, in that coordinate system is not W, it is W * cos(45 deg), and the equations correct for all of that.

Quote

So here's the rub...why can't we duplicate them or even come close in the case of the power-on numbers without this engineering approach?


I think some of it might be due to not feeling the g's, so in level flight, we aren't aware when we are pulling 1.2 g's vs. 1 g, etc., and it is because the literature varies and, in some cases, has inconsistencies or lack of data (like what weight the stall is at, what power setting the engine is at, and especially is it indicated or calibrated airspeed).

The AH F4U-1 seems to agree very well with the pilot's manual, and the F4U pilot's manual seems pretty good (unlike, say, the F6F pilot's manual, which seems pretty crappy in data quality).  Over time, I'll do some more testing and see what I get for other aircraft.

Offline Brooke

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Stall Speed Bug?
« Reply #67 on: January 28, 2007, 08:22:11 PM »
Summary:  For P-38J, clean, power off has excellent correspondence; dirty, power off is different by 9 mph.

From PILOT'S FLIGHT OPERATING INSTRUCTIONS FOR ARMY MODELS P-38H SERIES, P-38J SERIES, P-38L-1 L-5 AND F-5B AIRPLANES, on page 28, we get that the stall speed in clean condition, power off is 100 mph indicated, and for flaps and gear down, power off, 74 mph. From page 33, we get a table for calibrated airspeed. From the lowest two speeds in the chart, for clean, we get CAS = 0.870 * IAS + 27.8; for dirty, we get CAS = 0.741 * IAS + 34.1. Thus, clean, power off is 115 mph calibrated, and dirty, power off is 89 mph calibrated. This is at 17,000 lbs gross weight.

In Aces High, at 16,360 lbs gross, we ride the stall at 109 mph CAS (113 mph true) and 2700 fpm = 30.7 mph descent. cos(theta) = sqrt(1 - 30.7^2 / 113^2) = 0.962. v_stall = sqrt(1 / 0.962) * 109 = 111 mph calibrated. At a weight of 17,000 lbs, v_stall = sqrt(17000 / 16360) * 111 = 113 mph calibrated. So, Aces High and the Pilot's manual are only 2 mph different for clean, power off.

In Aces High, at 15,724 lbs gross with gear and flaps down, we ride the stall at 91 mph calibrated (93 mph true) and 2700 fpm = 30.7 mph descent. cos(theta) = sqrt(1 - 30.7^2 / 93^2) = 0.944. v_stall = sqrt(1 / 0.944) * 91 = 94 mph calibrated. At a weight of 17,000 lbs, v_stall = sqrt(17000 / 15724) * 94 = 98 mph calibrated. So, Aces High and the Pilot's manual are 9 mph different -- not as close.

Offline Badboy

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Stall Speed Bug?
« Reply #68 on: January 29, 2007, 01:59:03 AM »
Quote
Originally posted by Brooke
(well, there is sin(alpha) of it in the lift direction, but that is negligible for WWII aircraft)


Hi Brooke,

Mace2004 is correct, there is always a thrust contribution to lift, and for modern fighters it can't be ignored. I agree that for WWII fighters with very low T/W ratios its omission represents a small error of less than 1% which is negligible, but may account for part of the difference you are seeing in your results.

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Offline Brooke

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Stall Speed Bug?
« Reply #69 on: January 30, 2007, 12:50:04 AM »
Quote
Originally posted by Badboy
Hi Brooke,

Mace2004 is correct, there is always a thrust contribution to lift, and for modern fighters it can't be ignored. I agree that for WWII fighters with very low T/W ratios its omission represents a small error of less than 1% which is negligible, but may account for part of the difference you are seeing in your results.

Badboy


Yep, there is a thrust component to lift in the coordinate system I picked of T * sin(phi) where phi is angle between thrust centerline and direction of travel of the aircraft.  I ignored that in my calculations, but you guys are right, it might not be negligible.

For example, angle of incidence of wings in WWII aircraft is about 1-2 degrees, and max angle of attack (at stall) is about 12 degrees clean and about 8 degrees with full flaps, so phi_max is about 11 degrees, say.

From propeller theory, T = 550 * HP * eta / v, where T is thrust in lbs, HP is the engine HP, eta is the propeller efficiency, and v is the velocity of the aircraft (in ft/sec).  Typical total propeller efficiency is about 0.85.  For the F4U-1, HP is about 2000 HP and speed at stall for a 11,500 lbs F4U-1 is about 100 mph true = 147 fps, and we get thrust to be 6360 lbs.  Then sin(11) * T/W = 0.106, which could be significant.

I'll take a look at how it all rolls out in the equations.

Offline Badboy

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« Reply #70 on: January 30, 2007, 01:18:28 AM »
Quote
Originally posted by Brooke
From propeller theory, T = 550 * HP * eta / v, where T is thrust in lbs, HP is the engine HP, eta is the propeller efficiency, and v is the velocity of the aircraft (in ft/sec).  Typical total propeller efficiency is about 0.85.  For the F4U-1, HP is about 2000 HP and speed at stall for a 11,500 lbs F4U-1 is about 100 mph true = 147 fps, and we get thrust to be 6360 lbs.  Then sin(11) * T/W = 0.106, which could be significant.


Hi Brooke,

Don't forget that 85% is only going to be true at a point near to the top end speed. Near the stall the prop efficiency for the F4U is probably much closer to 60% and may be lower. I'm about to leave for work, I'll check my prop charts when I get back. But I'd say at the stall you are probably looking at a T/W closer to 0.4 or below and that reduces your figure from 0.106 to 0.07.  

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Offline Brooke

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« Reply #71 on: January 30, 2007, 01:30:46 AM »
Good point, Badboy.  I'll work on taking that into account, too.

Offline Badboy

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« Reply #72 on: January 30, 2007, 02:55:08 PM »
Quote
Originally posted by Brooke
Good point, Badboy.  I'll work on taking that into account, too.


Here is a prop chart for the F4U-1 that you might find helpful...



At 100mph (close to the stall speed) the advance ratio is 0.55, so the efficiency can be read from the chart at 59% just a little less than I thought. But I think the AH flight model gets it a tad closer to 60% at that speed. You will notice that the maximum efficiency in this configuration is just over 83% at an advance ratio equivalent to about 300mph.

The Aces High flight model just gets better and better, as we get better and better at measuring it :)

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Offline Widewing

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« Reply #73 on: January 30, 2007, 07:07:12 PM »
Quote
Originally posted by Brooke
Yep, there is a thrust component to lift in the coordinate system I picked of T * sin(phi) where phi is angle between thrust centerline and direction of travel of the aircraft.  I ignored that in my calculations, but you guys are right, it might not be negligible.

For example, angle of incidence of wings in WWII aircraft is about 1-2 degrees, and max angle of attack (at stall) is about 12 degrees clean and about 8 degrees with full flaps, so phi_max is about 11 degrees, say.

From propeller theory, T = 550 * HP * eta / v, where T is thrust in lbs, HP is the engine HP, eta is the propeller efficiency, and v is the velocity of the aircraft (in ft/sec).  Typical total propeller efficiency is about 0.85.  For the F4U-1, HP is about 2000 HP and speed at stall for a 11,500 lbs F4U-1 is about 100 mph true = 147 fps, and we get thrust to be 6360 lbs.  Then sin(11) * T/W = 0.106, which could be significant.

I'll take a look at how it all rolls out in the equations.


I like Diz Dean's simplified equation as it is more easily applied and understood by non-engineers by using mph instead of ft/sec.

Thrust = 375 x prop efficiency x horsepower / speed.

Naturally, you need to know the available hp and the efficiency of the propeller. Horsepower can be found in commonly available tables. Prop efficiency is tougher to determine. For max thrust at max level speed, you can fudge it some and simply use 80%. This will produce a reasonable "ball park" figure that is useful when comparing various aircraft.

For the F6F-5, flying at Normal power (44 in/hg @ 2550 rpm), the engine is making 1,675 hp at 5,500 feet (very near to the altitude I was testing at).

Thus, 375 x .6 (60%) x 1,675 (hp) / 88 (speed in mph) = 4282.67 lb

Using the normal equation:

550 x 1,675 x .6 / 129.0666 = 4282.67 lb

So, when flying 20 degrees nose up, less 3 degrees (F6F-5 incidence) we can calculate: Where T = 4282.67, W = 10,980
sin(17) x 4282.67 / 10,980 = 0.114 !!

This, I think, tends to account for the lower stall speed when flying into a stall at higher AoA.

My regards,

Widewing
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Offline Brooke

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Stall Speed Bug?
« Reply #74 on: January 30, 2007, 09:48:27 PM »
Good points, Widewing.

The formulas I'm using, though, are all in the coordinate system of the airplane.  Thus, in T * sin(phi), phi isn't the angle between line of thrust and the horizon, it's the angle between line of thrust and direction of travel (it is basically angle of attack minus angle of incidence of the wings, so alpha - 2 degrees or so).

All of this will not affect the power-off numbers where T is taken to be approximately zero.  (More accurately, in AH, it is probably a small negative number, but I suspect it is still negligible in magnitude.)