Some New Data Carts to chew on

[HoHun]

Hi Gripen,

>As Wells noted we are interested about thrust/drag/weight(mass) relations not directly about power.

The point I was trying to investigate is the relation between excess power of aircraft with a different speed of best climb, so the power balance chart was the way to go.

As Wells and you both pointed out, the shape of the thrust graph of course is different from that of the power graph. From each aircraft's best climbing speed, initial acceleration would be quite different, with the slower aircraft of course acclerating more quickly if their climb rates are similar.

However, what the power curve tells us is that when estimating acceleration at equal speed in the climb speed range from the climb rate, the exact speed of best climb will make little difference.

>there are big differences between best climbing speeds like in the case of the P-38 (around 160mph IAS) and P-51 (around 200mph IAS)

At sea level, that's 71.5 m/s true air speed for the P-38 and 89.3 m/s true air speed for the P-51. You can see from the above diagram (best climb speed 76 m/s) that the span between the two is easily on the plateau where excess power changes little.

Comparing sea level climb rates of 3730 fpm for the P-38J to the 3410 fpm for the P-51B, it safe to conclude that the P-38 accelerates better at the P-38's speed of best climb - judging from the above graph, the P-51 might lose about 5% of its climb speed by going slower, leaving the P-38 with a 15% advantage in climb/acceleration.

At the P-51's speed of best climb, the aircraft are matched closer - it's the P-38 that loses about 5% of its climb rate there, leaving it with a meagre 4% advantage in climb acceleration.

At even higher speeds, excess power drops faster, so I would expect the P-51's acceleration to match and finally exceed that of the P-38J's somewhere between 200 mph and 240 mph.

>also altitude can make a big difference

I think the biggest impact of altitude is by the different power characteristics of the aircraft engines. If you have climb rates at equal altitudes, you still can compare them with good confidence to estimate the relative acceleration (in the climb speed region).

Regards,

Henning (HoHun)

[gripen]

HoHun,
Well, excess power is not what we are looking for because the propeller is the limiting factor despite what ever amount of power is available. Anyway, I admited allready that it is possible to get acceptable idea of relative acceleration of the planes from the climb rates at climb speeds and your conclusions are pretty well in line with the real world tests (except that you appear to use military rating values for the P-51 and WER values for the P-38). At higher altitude the P-51 reaches acceleration of the P-38 faster because it has relatively  more thrust available at higher speeds (exhaust thrust and better propeller efficiency).

But earlier you wrote that:
>Acceleration from low speed can be estimated from climb rate with good accuracy

So how can you estimate accurate acceleration (value of m/s2) at given speed using just climb rate and speed without knowing drag/thrust/mass combination?

gripen

[HoHun]

Hi Gripen,

>Well, excess power is not what we are looking for because the propeller is the limiting factor despite what ever amount of power is available.

I guess had should have stated more clearly that the available power curve in my diagram accounts for propeller efficiency, too.

>(except that you appear to use military rating values for the P-51 and WER values for the P-38)

For the sake of the example, I was using the values from F4UDOA's performance sheet.

>So how can you estimate accurate acceleration (value of m/s2) at given speed using just climb rate and speed without knowing drag/thrust/mass combination?

A climb rate for a certain condition is equal to the aircraft's specific excess power for the same condition. Specific excess power has weight (and thereby, indirectly, mass) already figured in:

Ps=P/(m*g)

Newton tells us:

P=Fv; F=ma => a=F/m=(P/v)/m=(P/m)/v

With:

Ps=P/(m*g) => Ps*g=P/m

this results in our acceleration formula:

a=(Ps*g)/v   {edited to fix a typo}

Instanteous acceleration at best climb speed at sea level is 2.6 m/s^2 for the P-38J, compared to 1.9 m/s^2 for the P-51B at its best climb speed.

This is absolutely exact, but (unfortunately) not terribly useful since the speed of best climb differs :-)

Here's where the estimate that specific excess power at low speeds is fairly constant comes into play:

The P-51B can be estimated to have 95% of its climb rate at the best climbing speed of the P-38J: At 160 mph, the P-38 accelerates at 2.6 m/s^2 compared to just 2.3 m/s^2 for the P-51.

Likewise, at 200 mph, the P-38 accelerates at 2.0 m/s^2 compared to 1.9 m/s^2 for the P-51.

I'll also add in the F4U-1, which seems to have its best climb speed at 135 knots and accordingly accelerates at 2.1 m/s^2 at 160 mph and 1.7 m/s^2 at 200 mph.

Regards,

Henning (HoHun)

[ 01-05-2002: Message edited by: HoHun ]

[Dwarf]

Wonderful discussion, guys.

Couple of observations -

The P-38 reportedly achieved virtually identical climb rates at everything from 140 mph to 180 mph.

I have read that the F6F achieved its best ROC at 140.  However, the high AoA at that speed led to engine airflow problems and overheating, which forced testing and performance verification to be done using a climb speed of 160.  This resulted in lower ROC numbers than it should have (and was) capable of achieving.  Not sure if the F4U had similar cooling problems at its best climb speed, but it seems reasonable that 135 is slow both from a cooling and a torque management standpoint.

I offer both points as cautions that the starting lines aren't always where we think they are.

Dwarf

[Guppy]

Thanks for that, Dwarf. Interesting post.

The P-38 pilot's manual gives best climb speed as around 160 mph for ferry climb (2,300 rpm & 35" MP) and 180 mph for combat climb (3,000 rpm & 54" MP) at sea level for the H/J/L models.

[ 01-05-2002: Message edited by: Guppy ]

[bolillo_loco]

guppy, what is the weight listed for the 38H in the take off and climb chart?

[Dwarf]

Originally posted by HoHun:


a=(Ps*g)/v

I don't like to question your equation, but is it really stated in the correct form?

I believe, as written, the equation says that when g = 0, a = 0 ???

Even more, it says that if g is negative you decelerate, and that if g is greater than 1 you accelerate faster.

Clarify please.

Dwarf

[ 01-06-2002: Message edited by: Dwarf ]

[SageFIN]

I believe that g ~ 9.81 m/s^2 in Ho-Huns equation. A constant, that is.

[HoHun]

Hi Dwarf,

>I believe, as written, the equation says that when g = 0, a = 0 ???

As Sagefin pointed out, g is a physical constant, the standard gravitational acceleration of 9.81 m/s^2.

g=0 would imply the absence of gravity, which would make the concept of "climb" pretty difficult due to the absence of a concept of "up" ;-)

But if you'd be flying on the Mars with lower gravity, the same aircraft would have a higher specific excess power in the same flight condition (assuming an atmosphere identical to that of the earth). However, level acceleration would be identical to the value achieved under identical conditions here on earth. Specific excess power already accounts for gravity.

I admit that I should have explicitely defined the meaning of g. It's not the current "G-rate", which I'd note as "load factor n".

Load factor does of course have an impact on acceleration as well - "unloaded" dives with n=0 result in better acceleration due to reducing induced drag to a minimum. The interesting thing is that the benefit of "unloading" is greatest at low air speeds (which would require a large angle of attack to sustain straight flight) - at higher air speeds, the benefit of unloading pretty much vanishes.

Regards,

Henning (HoHun)

[Guppy]

bolillo_loco,

The P-38H in the climb chart portion of the manual is listed with a base weight of 16,100 lbs, corresponding to a military power climb rate of 3,500 fpm at sea level. Best climb speeds (IAS) are given as 178 mph combat and 151 mph ferry at sea level, and do not vary with weight (data provided for weights of 16,100, 18,100 or 19,500 lbs).

The P-38J/L are listed with somewhat higher best climb speeds--180 mph combat and 160 mph ferry at sea level.

[Daff]

"but a closer look to the AHT's data revealed that there is an error in the ammo loadings for the P-47D, ammunition should weight about 1057lbs not 664lbs"

There was two standard loadouts for the P-47 (Although varied a lot in the field): 267rpg or 425rpg.

Daff

[Dwarf]

Originally posted by HoHun:
Hi Dwarf,

But if you'd be flying on the Mars with lower gravity, the same aircraft would have a higher specific excess power in the same flight condition (assuming an atmosphere identical to that of the earth). However, level acceleration would be identical to the value achieved under identical conditions here on earth. Specific excess power already accounts for gravity.

Regards,

Henning (HoHun)

Gravity or load factor?

Isn't the real defining variable for Ps drag?

I'm feeling my way here, but it seems to me that acceleration involves more than simply power to weight.  And that climb and accel. while similar, aren't really equivalent.

To maximize climb, you put the aircraft in the attitude that maximizes L/D and go to full power.  To maximize acceleration, you put the aircraft in the attitude that minimizes total drag and go to full power.  Not the same attitude.  Not the same drag.  And not really the same value for Ps either.

Max accel in level flight would be yet another drag state, and a third different value for Ps, no?

Dwarf
[42 edits later I *think* I've said what I mean as clearly as I can - sheesh]

[ 01-06-2002: Message edited by: Dwarf ]

[HoHun]

Hi Dwarf,

>Isn't the real defining variable for Ps drag?

The definition is

Ps=Pe/W=Pe/(m*g)

with

Pe excess power, W weight, m mass and g gravitational acceleration.

Pe is a complex value determined by many factors including drag, but instantaneous acceleration and climb rate are directly interdependend as outlined above.

>Max accel in level flight would be yet another drag state, and a third different value for Ps, no?

Ps is defined for a specific flight condition, so in level flight at the defined speed, Ps for acceleration is the same as for climbing.

"Unloading" is a different flight condition that would give slightly different results, but comparing different airframes, the change of the flight condition will have a very similar effect, so that acceleration in unloaded flight will have the same relation as acceleration in 1 G flight.

It's certainly safe to say that an aircraft with a 10% climb rate advantage will have an advantage in unloaded dives, too.

Remember that aircraft weight varies with fuel loading anyway - we don't really need to care much about variations in the 5% magnitude since a WW2 fighter may easily be 10% lighter on low fuel than on full fuel anyway.

Regards,

Henning (HoHun)

[gripen]

HoHun,
Very neat indeed! I tried it for couple spreadsheet systems I made some time ago and your system appear to work well. I have used traditional calculation ie:

Drag at given speed
Fd = ½ * s * v² * A * Cd

In the case of the P-51B at sealevel and 200mph  (from various RAE and NACA papers):
s = airdensity at sea level = 1,225kg/m3
v = 89,4m/s
A = drag area = 2,265m2
Cd = generic Drag coefficient for complete plane at Cl=0,2 and below mach 0,6 = 0,2

Thrust at given speed
Ft = e * Pp/v + Pe
e = efficiency generic = 0,8
Pp = engine power from propeller same as you used 1510hp = 1109850W
Pe = generic exhaust thrust 120kp = 1177N

Useable thrust for acceleration:
Ft-Fd = 8891N

Acceleration:
8891N/4219kg = 2,1 m/s2 (WER results 2,3 m/s2)

Well, it's pretty near your values, anyway it was propeller efficiency why I gave up with this system at past. At sea level this system is pretty accurate, I can estimate even top speed quite well. But at above 10k this system appear to be more and more unaccurate and overall this system need very good data which is rare.

gripen

[Dwarf]

Originally posted by HoHun:
Hi Dwarf,

Ps=Pe/W=Pe/(m*g)

with

Pe excess power, W weight, m mass and g gravitational acceleration.

Regards,

Henning (HoHun)[/QB]

This would seem to account for inertia, but not drag.  And, inertia isn't the whole story either.

I just don't see how Ps can be the same for both climb and accel, when those two states have, as they must, different Drag values.

After all, it's the increase in Drag more so than the decrease in Thrust that reduces Ps to 0 at some point.  Thrust decreases linearly while Drag increases exponentially with increasing velocity.

Plus, you can't determine Ps until you define the desired outcome.  Do I want to climb, or do I want to accel?  Whichever it is, I must first create the necessary drag state before I can find out whether I even have any Ps, let alone what its value might be.

I would agree, that at the margins, Ps would be the same for both climb and accel, but for the vast middleground between Stall (actually, sitting still) and Max Level Speed, I don't believe that identity would hold.

Dwarf

[ 01-06-2002: Message edited by: Dwarf ]