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V2 vs. weight vs. climb question

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Old 25th Nov 2011, 13:20
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Angel V2 vs. weight vs. climb question

I probably should have posted this here first but, risking a breach of forum etiquette, I'll re-post the thread here:

http://www.pprune.org/biz-jets-ag-fl...-more-huh.html

Summarizing the scenario: I have a Gulfstream III (G-1159A) at its MTOM of 69,700 lbs. (Please, no correction or discussion of weight in lbs. vs. mass in kg. needed ). It has been noise certificated as a Stage 2/Chapter2 airplane per this procedure from the AFM:

GIII Noise - Trolltune Corporation

164 KIAS (which = 164 KCAS/KEAS at sea level ISA) is V2+10 at MTOM.

Now, I decide to reduce MTOM to 61,500 lbs and climb at V2+20. Note that V2+10 at HW equals V2+20 at LW (164 KIAS), where LW = low weight, HW = high weight. What is the effect on climb? According to responses in the other biz-av thread, I can expect an increase in deck angle, climb angle, and climb rate. Although that sounds counter-intuitive, are we perhaps getting closer to (the airspeed we seldom discuss for such an airplane) Vy?

I have the G-III AFM but would like to quantify the changes after understanding the core answers to the question.

Your thoughts are appreciated.

Cheers,

Tom
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Old 27th Nov 2011, 16:33
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I'll have stab at this.

Climb rate will be higher that is a given, you are lighter and at V2+20 you are still slower than VY. It is only when going faster than VY than you will get lower climb rates at higher speeds and negate the lower weight effect.

At the same speed, your climb rate will increase by RC2=RC1*W1/W2 so that is an increase of 13%. At V2+20 you will be closer to VY and further increase your climb rate.

Climb angle will be higher at lower weight too. VX is not very far from V2 (typically) and at V2+20 you are going to have a lower climb angle than at V2+10 for the same weight. However at VX weight is overwhelmingly more predominant than drag so the 10 knots speed increase is very unlikely to affect climb angle as much as weight.

So, climb angle higher too.

Deck angle well that depends on whether the higher climb angle more than compensates the lower angle of attack. You do have a lower angle of attack at V2+20 LW since you are lighter and you go faster. Maybe a bit more than one degree lower (napkin says sqrt(69700/61500)=0.94 or 6% lift coefficient reduction or about 0.1 and at 1 degree per 0.1 CL so that is one degree AoA just for weight decrease plus some fraction of a degree for the speed increase).

Assuming the 10 knots effect on climb angle is much smaller than the effect of weight, the climb angle increases by the ratio of weight or 13%.

So if you have a climb angle of 15 degrees at HW, you'll get a climb angle at LW of 13%*15 = 2 degrees more.

And one degree less AoA.

So a deck angle one degree higher. But it is a close call.
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Old 28th Nov 2011, 01:54
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I am certainly not a jet expert, but I know a little about the concepts associated with noise testing. Though I don't completely understand the question here, it seems to be associated with the noise footprint being made by the plane.

All other things being equal, the best rate of climb performance will get you the farthest away from earth in the least time. To keep the noise footprint small, you want to get the plane away from the ground as soon as possible. (assuming engine noise is otherwise not changed). Best rate of climb speed clears obstacles better, but the lower speed and climb rate leaves a larger footprint of noise.

There is a lot written about noise testing, and some of the theories behind it.

Perhaps some of these issues are factors in your question?
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Old 2nd Dec 2011, 00:54
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Angel Machdiamond's "stab at this"....

Machdiamond, thanks very much for your considered response and answer. It is appreciated.

A few additional thoughts/questions:

".....you are still slower than VY".

Yes, I can appreciate that. Looking at the AFM, it seems that 10 deg flap sea level climb gradients at 164 KIAS are about 6% at 69,700 lbs, going to about 8% at 61,500 lbs., resulting in some surprisingly low climb rates (1050 to 1350 fpm or so, is that right?). Yet, the AFM Time-to-Climb tables from 0 to 5000 feet at 250 KIAS show almost 4000 ft/min! Does that mean Vy is closer to 250+ ??

"At the same speed, your climb rate will increase by RC2=RC1*W1/W2"

I'll buy that, but with a reservation that your formula only covers an inertial climb effect. I would expect that a slight reduction in induced drag at the lower weight would contibute just a little more RC, no?

"At V2+20 you will be closer to VY and further increase your climb rate."

I see where you're coming from, but if V2+10 at the higher weight (164 KIAS) is equal to V2+20 at the lower weight (also 164 KIAS), does this remain true? I can see that you're probably correct.

"....at V2+20 you are going to have a lower climb angle than at V2+10 for the same weight."

That sure sounds right to me.

"....at VX weight is overwhelmingly more predominant than drag so the 10 knots speed increase is very unlikely to affect climb angle as much as weight."

That sure sounds right to me as well.

"Deck angle well that depends on whether the higher climb angle more than compensates the lower angle of attack. You do have a lower angle of attack at V2+20 LW since you are lighter....."

Yes, I agree.

"....and you go faster."

Not sure, since even at LW I'm not really "going faster", I'm still at the same airspeed. Is your following AOA and "napkin" result still valid?

"Assuming the 10 knots effect on climb angle is much smaller than the effect of weight, the climb angle increases by the ratio of weight or 13%."

That's interesting, can it really be that simple?

"But it is a close call."

I do appreciate that, and also the time you've taken to enlighten me. Please comment again if you find the time.

Cheerio,

Tom
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Old 2nd Dec 2011, 01:46
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Angel

Hi Pilot DAR. Thanks for your input.

"All other things being equal, the best rate of climb performance will get you the farthest away from earth in the least time."

Agreed 100%.

"To keep the noise footprint small, you want to get the plane away from the ground as soon as possible."

Well, yes and no. It's certainly true that the further "up" you are, the better. Small piston engined airplanes do indeed use Vy to reach the noise measurement point (constraint) that is 8200 ft from brake release. Jet aircraft, however, use an airspeed closer to Vx (typically V2+10 to V2+20) and reach the noise measurement point (constraint) at 21,325 ft from brake release. They're allowed one thrust cutback after a certain altitude but no configuration change (e.g., flaps) other than gear retraction. So in this case, Vy may not be appropriate since you might think of the noise measurement point as an "obstacle".

"Best rate of climb speed clears obstacles better....."

I'm sure you meant to write "Best angle of climb speed clears obstacles better....."

Comments invited.

Cheers,

Tom
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Old 2nd Dec 2011, 13:35
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Tom,

"Does that mean Vy is closer to 250+ ?? "

That's what I'd expect for this class of aircraft.

"I would expect that a slight reduction in induced drag at the lower weight would contibute just a little more RC, no?"

Yes although as you say: just a little more.

"Not sure, since even at LW I'm not really "going faster", I'm still at the same airspeed. Is your following AOA and "napkin" result still valid?"

Yes it is, should have said same airspeed.

"That's interesting, can it really be that simple?"

Yes. The real equation is sin(gamma)=(T-D-aW)/W so assuming T(thrust) D(drag) and a(longitudinal acceleration to maintain constant indicated speed) are all unchanged or negligible in the case of a, we get sin(gamma1)=constant/W1 or sin(gamma1)/sin(gamma2)=W2/W1 in other words the climb gradient increases by the ratio of weights.

Of course a is not really negligible and D is a bit smaller but the approximation gives a good idea of the change as long as we deal with similar speeds.
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Old 2nd Dec 2011, 15:22
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Angel

Superb, Machdiamond! Great stuff.

Thanks for spending your time on this. I've learned a lot.

All the best,

Tom
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Old 3rd Dec 2011, 13:27
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Never heard of Vy being part of a noise abatement procedure-always V2 plus 10 unless i am missing something
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Old 3rd Dec 2011, 14:08
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No one said VY had anything to do with noise abatement, only that V2+20 is closer to it than V2+10.
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Old 3rd Dec 2011, 17:13
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Angel

Hello Pull what.

As Machdiamond stated, Vy is not a goal here, just a reference destination. When he writes:

No one said VY had anything to do with noise abatement, only that V2+20 is closer to it than V2+10.
I would add the qualifying statement "at the same weight" because V2 decays with lower weights.

I should clarify a couple of things. First, this is not about noise abatement, it's about noise certification, two very different animals. Certification procedures dictated by the airworthiness folks are certainly not the nicest way to please the neighbors at all. But they are standardized.

The GIII of which I write was originally noise certificated at its MTOM of 69,700 lbs at V2+10 which is 164 KCAS. The regs allow noise demonstrations to be flown in the window of V2+10 to V2+20 as selected by the applicant.

So, what's my dilemma? For some peculiar, but unrelated reasons, I need to re-certificate the airplane with a lower weight limitation. But I do NOT want to re-do noise flight testing for two important reasons:

1. It costs way to much.
2. The airplane won't pass based on current regulations.

Back in the '80s, thrust cutback was allowed when measuring sideline noise level (450 meters laterally from TO path at its noisiest). Even then, it just sqeaked by. Today, thrust cutback isn't allowed until deep into 2nd segment climb for the TO/flyover measurement.

But, surely you say, at lower weight, climb is better and noise is less, no? Not necessarily. Certainly true for TO and approach measurements, but sideline noise usually increases. As counterintuitive as that may seem, it is because jet transport noise is measured in an EPNdb scale which includes a duration of exposure or time element. V2+10 for the GIII, say at 61,500 lbs, is 154 KCAS or ten knots less than the certificated airspeed. FAA/TCCA/EASA/UKCAA/ICAO et al will all suspect a noise increase of 0.1 EPNdb or more given the longer "dwell" time in the fly past. Any such increase leads to a full scale noise testing program.

What to do? Fly at V2+20 which is now the original airspeed, hence no sideline issue. Hopefully the noise police would agree that represents "no acoustical change" (NAC) and I can move forward.

I guess that's a rather lengthy missive and perhaps more than you cared to read. My post here was to hopefully get some help about climb path performance calculations so that I can determine the TO/flyover altitudes 6500 meters from brake release, using different airspeed and weight combinations. The AFM is unhelpful in that regard, since it focuses primarily on operational V1, V2, Vr speeds and net climb gradients. Machdiamond has been of great help, but looks like I still need to dig a little deeper. Being able to figure out the geometry/TO profile the way Gulfstream first flew it (I posted the procedure above) would be a good start.

Felt good to get that written, even if no one reads it.

Bests,

Tom
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Old 5th Dec 2011, 17:29
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I read the whole thing

To me it sounds like (pun intended of course) you do have a valid case to present to the certification agency. Your climb angle will be higher, it is a fact of life. At the same dwell time, that means you will be quieter.

A simple statement to that effect should be sufficient, there should be no need to demonstrate this by flight test or by analysis. Maybe you will need a Flight Analyst DER (or whatever they are called in your neck of the woods) to write that statement for you, it should not take more than 5 minutes of his time.
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Old 5th Dec 2011, 17:56
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Angel

Thanks Machdiamond. Agree with what you wrote, and appreciate your comments.

Cheers,

Tom
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Old 6th Dec 2011, 10:27
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Considering that the G3 has a cumulative noise level of stage 3 +10 EPNdB, so are you going to achieve significant noise reductions to make your efforts worthwhile?

Mutt
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Old 6th Dec 2011, 16:59
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Angel

mutt, good to hear from you again.

Well, that's a good question and what I'm working to find out. The GIII's cumulative noise margin beyond Stage 3 is actually 9.3 EPNdb - 2.1 above TO, 8.6 above sideline, and a credit of 1.4 beating Stage 3 on approach.

As long as I can show NAC and avoid noise testing, the only one I really care about is a reduced flyover/TO noise, and I'm hoping to get that down considerably with weight reduction. Not too much, obviously, because I'm chipping away at the airplane's utility. I'll know more when I've figured out the TO path/profile comparisons.

Bests,

Tom
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Old 12th Dec 2011, 11:39
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Hello,

My first post out there.

The climb gradient can be easily computed with

thrust to weight ratio - Cd/CL

Decreasing the weight will of course increase the climb gradient.
increasing the speed has several effects:
  • decrease the thrust (negative effect)
  • depending on where you are on the A/C polar, your lift to drag ratio may increase or decrease
  • The critical case in which we usually compute climb gradients is the engine failure case : the higher the speed, the lower the need of rudder deflection, which will reduce the penalty in drag and improve climb performance.
It's all a matter of CL versus Cd curve.


Now for the A/C pitch, it's the sum of the AoA and climb gradient (or groundslope). You don't necessarily have a lower pitch at V2+10 since you may reach a higher climb gradient than at V2, for a very low decrease in AoA.





For the vertical speed, I won't learn anything to anybody by writing:
Vz=TAS*climb gradient.


Lets say you have your optimum climb gradient at 1.2Vs (wonderful, at V2), you won't have your best vertical speed at V2, you may find it at speeds between 1.3 to 1.5 Vs, depending on the A/C type (turboprop or turbojet, wing polar...)



all the best
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Old 12th Dec 2011, 18:49
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Angel

chti guillaume,

First of all, as an "old timer" [NOT!] around the forums, please allow me to welcome you.

Your input is very interesting and I appreciate your thoughts very much. I will need to study your ideas carefully, as I'm not confident that I understand all of the relations you've put forward - yet.

Regardless, it's very kind of you to respond and I'm particularly happy that you chose to make this topic the first of what I can only hope will be many future posts.

Very best regards,

Tom
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Old 12th Dec 2011, 20:19
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Hello

I'm not a specialist of turbojet airplanes but I'm glad these few explanations helped and brought further questions.

The best would be to go to the performance guys I think they can show you:
  • The lift versus drag curves so that you can see the evolution of the lift to drag ratio for V2 (if you are not limited by 1.1 VMC at 61000lbs) V2+10 V2+20). I guess at V2 the lift coefficient would be CLmax/1.44
  • Check the engine thrust for these 3 speeds (lets say ISA - SL)
Then you can quickly hand compute the climb gradient and the vertical speed.


Getting back to your matters, at what distance from the end of the runway (and from the 35ft clearance) is the mic that measures the sound ? Is it far enough to clear the 2nd segment ? How is the noise measured, it's a matter of time and peak, or only of sound peak?




Chti Guillaume
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Old 13th Dec 2011, 18:33
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Angel

Chti, thank you.

The lift versus drag curves so that you can see the evolution of the lift to drag ratio for V2 (if you are not limited by 1.1 VMC at 61000lbs) V2+10 V2+20). I guess at V2 the lift coefficient would be CLmax/1.44
I have no idea what the L/D ratio is but I do have the GIII AFM. Can it be determined from this operational data?

Remember that I'm concerned only with one airspeed, 164 KCAS. This may be V2+10 or V2+20 or V2+whatever depending on weight, but it's always 164.


Check the engine thrust for these 3 speeds (lets say ISA - SL)
I've allowed myself the assumption that thrust decay vs. airspeed vs. some amount of ram recovery means I can estimate using initial "stub-thrust" values. I understand that's not 100% correct, but probably close enough. Even if I don't get the absolute values correct, it's only the proportional reference altitude differences at different weights that I'm after. And yes, ISA - SL is the benchmark I want to use.

Getting back to your matters, at what distance from the end of the runway (and from the 35ft clearance) is the mic that measures the sound ? Is it far enough to clear the 2nd segment ? How is the noise measured, it's a matter of time and peak, or only of sound peak?
The mic is at 6500 metres from brake release. At that point the airplane is in second segment climb, flaps 10, gear up, and a thrust cutback from EPR 2.51 to 1.86 has been made. You're quite right, for certification purposes it's time and peak (EPNdB), but I only care about single value peak (in dBA).

Meilleures salutations,

Tom
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Old 15th Dec 2011, 07:57
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Hello,

sorry I was'nt clear enough.

If you are at the same speed then you are totally right to say that the thrust is the same (for the little difference of ram recovery with inlet AoA, that's totally peanuts).

For the L/D ratio, I meant the lift to drag ratio, which gives for example the best glide speed.

What I wanted to say is that, even if you are at the same speed, the wing and the HTP are not at the same operating point (in terms of lift and drag coefficient), which may have an adverse effect. Of course, weight reduction will always win and the climb gradient will be better.

So, getting back to your initial question:

  • No matter the weight, CAS=164KT : thrust is the same. No effect
  • Weight is reduced : ++++ effect
  • Lift to drag ratio is changed : may be positive or negative.
if you approach your speed for best vertical speed by staying at 164KT and reducing the weight, your climb gradient will be lower, and you will clear the 6,500m mic at a lower weight : I guess you then have a noisier aircraft.


So my advice is to find out the lift coefficient at which optimum climb gradient is get, then calculate the margin to stall speed, and fly at this speed, provided it is not lower than V2.


I hope this is helpful to your matter.


send me a private message if you need more details , or maybe a few graphs.
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