Some New Data Carts to chew on

[wells]

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.

You are measuring an instantaneous acceleration at a certain speed.  The drag and thrust at that speed for 1G flight is the same, whether the plane is climbing or in level flight.

[Dwarf]

Gripen -

It's propellor efficiency that has consistently defeated me too.  All of the definitions (equations) I can find are circular.

Thrust depends on prop efficiency which depends on velocity which depends on Drag and Thrust.  

I could never seem to quit chasing my tail, and like you I have resorted to using a generic 80% for prop efficiency and call it good enough for government work.  But I'm far from satisfied with the results.

Dwarf

[Dwarf]

Originally posted by wells:


You are measuring an instantaneous acceleration at a certain speed.  The drag and thrust at that speed for 1G flight is the same, whether the plane is climbing or in level flight.

Only if you are willing to accept whatever climb rate falls out of merely firewalling the throttle.  Because if you don't adjust pitch, you will always climb and not accel.  And, even then, you won't climb at your best rate.

If you seek to maximize either climb rate or rate of accel, you need to first adjust your flight condition so as to permit a successful outcome.

Also, in order to reach any meaningful conclusions about relative performance of aircraft, we need to base the discussion on persistent conditions and not instantaneous ones, IMO.[edit] (except that persistent is an oxymoron... gaaaaaa      English is just so inadequate sometimes.     My gut says drag and inertia and maybe the way you hold your mouth all play a part, but proving it....)

Dwarf

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

[Dwarf]

To illustrate what I'm trying to get at -

Assume a heavily laden buff.

It staggers into the air.  If it gets cleaned up and keeps its nose down it has enough Ps to accelerate.  But, no matter how squeaky clean the pilot makes it, it does not yet have enough Ps to climb.

Why?  Because to climb it must increase the lift is is generating and that also increases the drag it must overcome.  In both cases, it would be operating at the same 1G load and be subject to the same inertia.  In both cases, the equations we have seen so far would yield the same  positive value for Ps.  However, that Ps number only has any practical value insofar as it allows the aircraft to reach a great enough velocity that it can begin to climb.  ie. (or is it eg.?) Ps is great enough to overcome added skin friction drag but it is not great enough to overcome added induced drag.

To recap: For all positive values of Ps, accelerating is an option.  But, for only some positive values of Ps is climbing an option.  

Thus Ps is merely a number, and its significance depends not on its magnitude, but on the problem at hand.  While climb and accel ARE similar problems, that similarity does not extend to equivalence in all cases.  Inferring performance in one regime from data developed about the other may lead to inaccuracies.  Or so it seems to me.

Dwarf

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

[wells]

It staggers into the air. If it gets cleaned up and keeps its nose down it has enough Ps to accelerate. But, no matter how squeaky clean the pilot makes it, it does not yet have enough Ps to climb.

If it can accelerate in straight and level flight, it can climb.

 

Why? Because to climb it must increase the lift is is generating and that also increases the drag it must overcome.

Yes, but only momentarily while G load > 1.0 in order to raise the nose to an angle who's sine is (T-D)/W.  Then, it's back to 1.0 G, climbing at a steady rate.

[Dwarf]

Originally posted by wells:


Yes, but only momentarily while G load > 1.0 in order to raise the nose to an angle who's sine is (T-D)/W.  Then, it's back to 1.0 G, climbing at a steady rate.

Indeed.  The problem, when you investigate induced drag closely, is that getting to that new AoA can involve a manyfold (manifold?) increase in drag.  While momentary, that spike is more than enough to kill you.

Point being that climb requires a higher initial value of Ps than accel.  Not because the requirements are different for the steady-state portion of the maneuver, but because Ps, alone, carries you over that drag spike and keeps you alive.

Dwarf

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

[HoHun]

Hi Dwarf,

>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.

Easy :-)

Pe=Ptotal-Pdrag

and

Ps=Pe/(m*g)

So the power necessary to overcome drag has already been subtracted earlier, and all power that's left can be used to either accelerate or climb.

For any specific flight condition, Ps for acceleration and climb is indeed equivalent.

Regards,

Henning (HoHun)

[Dwarf]

Originally posted by HoHun:
Hi Dwarf,

Easy :-)

Pe=Ptotal-Pdrag

and

Ps=Pe/(m*g)

So the power necessary to overcome drag has already been subtracted earlier, and all power that's left can be used to either accelerate or climb.

For any specific flight condition, Ps for acceleration and climb is indeed equivalent.

Regards,

Henning (HoHun)

OK.  We're getting closer to agreement.

     

I still go back to my point in the post above, though.

Once established in either the climb or accel regime, I think the two problems are indeed equivalent enough to not matter.  It's getting from where you start to that established condition that differentiates climb from accel.

Climb can charge a very high entry fee, while accel lets you through the gate for free.

Dwarf

Maybe this will help.  Refer to your diagram.
At Stall speed, Ps is very near its maximum but still increasing.  

Somehow, Drag is not being properly accounted for in order to generate that number.  Ps is more potential than actual at that point.  More hope than fact.  We won't know until we try to do someting whether we really have the Ps we think we do.

The numbers would lead us to believe that a pilot could do nearly anything he wished.  Climb, accel, or do Whifferdils.  How could he not?  He's got all the excess power anyone could hope for.  Yet, as nearly 100 years of flight has conclusively established, if he tries to do anything other than accelerate, he will crash and burn.

Meanwhile, up at the high speed end of the graph, one or more parts of that aircraft may encounter its critical mach speed and its attendant sharp drag rise before Ps decreases to zero.  Now, we have a situation where the aircraft can climb, but can no longer accelerate despite what the Ps number says.

Would somebody, please, hurry up and solve Navier-Stokes?    

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

[wells]

It's propellor efficiency that has consistently defeated me too. All of the definitions (equations) I can find are circular.  

Thrust depends on prop efficiency which depends on velocity which depends on Drag and Thrust.

Prop efficiency depends on power, prop diameter, velocity and density, that's it.  It can be found with a series of 3 equations.

Equation A:

X = V^3 * PI * density * diameter^2 /(2*Power)

Equation B:

Y = SQRT[(X/3)^3 + (X/2)^2]

Then:

e = (X/2+Y)^(1/3)+(X/2-Y)^(1/3)

That assumes no losses and there's always losses, so in your calculations, you can use 0.8 * e to get results within 2-3% for just about all cases.

[Dwarf]

Originally posted by wells:

Equation A:

X = V^3 * PI * density * diameter^2 /(2*Power)

Equation B:

Y = SQRT[(X/3)^3 + (X/2)^2]

Then:

e = (X/2+Y)^(1/3)+(X/2-Y)^(1/3)

That assumes no losses and there's always losses, so in your calculations, you can use 0.8 * e to get results within 2-3% for just about all cases.

One of my sources  does things a little differntly.  First, defining something he refers to as Power Coefficient.

The same source then defines a Thrust Coefficient in a similar manner and  uses those two terms in conjunction with Advance Ratio to define prop efficiency.

That whole shebang looks like this:

Advance Ratio: J = V/(n*D);

Power Coefficient: c(p) = P / ((density*n^3)*D^5)

Thrust Coefficient: c(t) = T / ((density*n^2)*D^4)

And Finally: (prop efficiency) = J * [c(t)/c(p)]

with P = 550 * brake horsepower
     D = prop diameter in feet
     n = prop rotational speed (revolutions per second)
     density = air density in a standard atmosphere at current operating altitude as expressed in slugs per cubic foot.  A slug being 14.59 kg or 32.174 lb(mass)
     T = thrust (lbs)

The kicker, of course is that you need an accurate value for T to get prop efficiency, and you need an accurate value for prop efficiency to get an accurate value for T.

Whichever set of formulas comes closer to being accurate, both would seem to contain more than enough error as to render Ps very suspect at the times when you need it to be most accurate.

Dwarf

[ 01-07-2002: Message edited by: Dwarf ]

[Dwarf]

wells -

As a test, I plugged a few values into your equations.

D = 10 ft
density = .001869 * 32.174 = .06 (8000 ft for the 3 folks whose eyes haven't already glazed over   )
P = 550000  (1000 hp)

For V I used both 250 fps and 300 fps.

Both times, after working the 3 equations thru fully, I arrive at a raw e value of 1.
Applying your fudge factor to that result, I wind up back at the generic 80% efficiency I was already using.

Maybe if I tried more values for V I might eventually get something *very* slightly less than 1 for an answer, but I very much doubt it.

It seems we're no closer to a meaningful prop efficiency than we were before.

Anybody else got a set of formulae that isn't circular (unlike the set I already had)?

Dwarf

[ 01-07-2002: Message edited by: Dwarf ]

[gripen]

Dwarf,
If you have a good data set on a propeller, you can build a deterministis model but as you can see, it's a case intensive solution.

gripen

[ 01-07-2002: Message edited by: gripen ]

[F4UDOA]

Heya's,

Go away for a couple of day's and the thread explodes.

Anyway I see things have gone beyond my level of understanding. However...

I still disagree that climb and acceleration are 100% directly proportionate.

For example. Burt Routan's Voyager has an extreme Aspect Ratio to maximize lift with minimal power. If you took the same design and reduced the aspect ratio to as low as you could and maintained the same power without increasing weight while still being a flyable Aircraft which would climb better and which design would accelerate better?

It is just an extreme example to prove the point I was trying to make. That you can't directly link climb and acceleration.

Here is another question.

Based on Thrust-Drag / Mass how would the same A/C acclerate?

[ 01-07-2002: Message edited by: F4UDOA ]

[wells]

For example. Burt Routan's Voyager has an extreme Aspect Ratio to maximize lift with minimal power.

This seems to be where you misunderstand.  Lift supports the weight of the plane.  It doesn't matter what the aspect ratio is, only what the wing area is.  What a high aspect ratio does, is minimize induced drag.  As you can see from the climb rate equation, when drag is less, excess thrust is more and the plane climbs better.  Or, the power required at cruising speed is less.

[wells]

Dwarf, for density, you should be using 0.00237 slug/ft^3