Sorry ShyTorque, no offence intended with abbreviation of your or anyone’s name.
True, I didn’t come back to you on the difference between Shear Forces (spelt correctly now) and Bending Moments, because one is a product of the other, they are closely related the bending moments create Shear Forces, and the Shear Forces break things. I just really don’t want to get into that, I’m sure you’ll understand.
Maybe a different thread? Or study the relationship yourself?
Lone
That’s a long post and it’s 98% correct, but somethings are a little nuanced in a way I’d like to come back on.
Para 1
Stall, I think we are talking about stall in the sense that for the whole disk the Coefficient of thrust has reach a maximum value, i.e. CtMax, I think most people are happy with that.
“we don’t know what the G load was” true, but my calculation puts it at 2.7g (21deg/s at 90kts is 2.7g), which is probably achieved at about CtMax, and if he had more capacity to pull g then he maybe would have used it. I accept that he (also) probably ran out of energy from the engine (engine power limit) and consumed some RRPM energy as well as Height Energy. According to NL’s excellent graph (from a different type) he had quite a lot of energy available, if (assuming) my speed calculation is close, accounting for the height he had, and the amount of time in which he spent it. 5sec of Max power is equivalent to at least 200ft (Energy), so he spent that height in 2 seconds equivalent to a lot of engine power (maybe 2.5 times), PLUS more than full engine power. One can infer that he was most probably at CtMax.
Para 2
Stall, call it what you like, but I mean running at CtMax. YES the CA is "an effect not a cause”, but it is related by relationship of TRT to Cf (is anyone disputing THAT?) CA=TRT/Cf. So far from being irrelevant, it tells us that for a given RRPM that the TRT is some multiple of Cf (which is a product of Nr^2). The key is even if the blades are going slowly the TRT that can be made is also less, as is the Cf (by the same proportion), so the CA is the same, drooped or not.*
Para 3
Yes also agree, but in this case the helicopter WAS doing about Vy (which as everybody here knows is the place where best use of energy is made to make TRT), so the amount of surplus Thrust that could be made was near it greatest.
Para 4
“AnFI's estimated are based on ground speed” good point, since it is airspeed that is important, and I did not assess the wind speed, so there is room for error there.
“If the Apache was below that airspeed as the final pitch and pull was attempted, it was already in energy debt.“ YES true “IF", but I say it was not below that airspeed (which could of course be wrong, but it is my working figure from my measurement, and if we work with THAT figure then it was not, according to you too). It doesn’t seem like the Airspeed reduced much, and was probably funded by height, but even if it was MY 90kts is an AVERAGE, so regardless of whether it burned KE or not there was quite a lot of energy around (AND he would have been pretty close to the flat bottomed curve of the "sweet spot”) (most surplus from the engine, and height (unmeasured) equivalent to substantial power over a 2 second period). I agree however that he was probably maxed on those too and did in fact also consume energy from the Nr as well (which you point out is not a low inertia rotor (so substantial energy derivable from Nr). He burned a lot of energy, and I think he was at CtMax, all (my) working numbers point at that (particularly 2.7g)
Para 5
Yes in gets hungrier for energy, (and if the Ct is already maxed, then the harder you pull the hungrier it gets, with no increase in TRT, so no additional G) ('Pull more get more party' is over) (at UCA)
Para 6
“Whatever angle the blades cone to is a reaction to that bundle of forces and effects on the disc/blades” Namely those detailed in Para 2 above, which make CA not irrelevant but a direct indicator of how much of the capacity of the Rotor is being used. Please don’t just glaze over at that relationship, it is fundamental. Ca=TRT/Cf
Para 7
Agree completely.
Punto
“AnFI has actually credited you [dc/da] with that, although you need a beady little eye to spot that in his posts. He now talks about a band of UCAs rather than a single UCA”
and challenge.
Yes I did, but I qualified it (as you rightly said) as being insignificant.
The reason I say it is insignificant is that it might be more significant in the illustrative thought experiment I presented of loading a hovering helicopter with progressively more weight as Nr is increased, such that CtMax is maintained, since indeed the IndFlow would change (and worsen the situation wrt CtMax), however this is much less relevant at speed where the increased Induced Flow with weight is much less significant. I said it was baby out with the bath water, not a First Order effect.
AND in any case and regardless, when CtMax is reached that also would be CAmax (UCA) (at a constant RRPM). Agree?
AND furthermore, I think the onus is on dc/da to quantify HIS point. I was asked to quantify mine and give assumptions, which I did, I am entitled to make my assumptions. I make the assumption that Increased Induced flow is not relevant, and under that assumption I presume dc/da agrees with me? QUESTION
The ‘family of UCAs' is in part developed through the discussion here, but also falls out of the maths too. e.g. it is dependant on density (linear), and it also is a function of the Ct fall off that NL gives with speed (in one of his excellent graphs).
“even though there may be a nugget of truth riding on the hobbyhorse.” quite a substantial nugget !
Ref ‘the Challenge’ from Punto I asked dc/da multiple times to quantify the term. It’s HIS objection, the onus was on HIM to substantiate it. It MIGHT be significant, quantify it, show us how significant it is. Is it the baby or the bathwater, is it a 'hair on the egg’? Or is it indeed a substantive point? PARTICULARLY at speed.
Does he agree that under the assumption of that effect not being significant the main point holds ‘true’?
The piece where he points to an Ω term on the bottom is (I say) wrong and highly distorts the significance of Ω.
I quote the piece here and explain why (I say) it is wrong below that.
dc/da
"Unlike a fixed wing, a rotary wing is rotary. Therefore the "v" that any aerofoil element experiences relies on rrpm and the element's distance from the hub let's say Ωr . However the downwash the element is seeing is independent let's call it u.
Therefore
α = arctan(u/ Ωr)
Assuming a small angle
α = (u/ Ωr)
And substitute
κ = ρ.A. (u/ Ωr).a /2m.
As you can now see, there is a term for rotor speed in your equation. Q.E.D. "
why that's wrong
Well the α term should say (P-u/ Ωr) where P is pitch
I don’t think you can leave out the Pitch of the blade.
So by substitution we have
κ = ρ.A. (P-u/ Ωr).a /2m
would expand out to
κ = (ρ.A. P.a /2m) - (ρ.A.(u/Ωr)/2m)
so the "κ = ρ.A. (u/ Ωr).a /2m" overstates the dependancy of κ on Ω, which is too naughty to say QED, and relegates it to an examination of the baby by looking at the bathwater.
AND in any case THAT also assumes that P is not varied, which is NOT a fair assumption.
AND furthermore where u is negligible as in the case of a helicopter pulling out of a dive at 90kts, then the term almost disappears.
AND furthermore in the ‘thought experiment’ of increasing the Nr and increasing the weight correspondingly the u value WOULD NOT be independent of Ω, but it would be dependant on it, thus reducing the assumed error further (to zero, by cancelling)
So while I do freely admit the proposed relationship MAY NOT be EXACT, I do say that any difference is just bathwater and not a substantive point. Quantifying the difference might be quite complex and subtle, but at least we can say it is comparatively small.
So I say that my point (whatever it was) still holds ‘in essence’.
AND the onus would be on dc/da to substantiate his objection otherwise.
So with respect to the Challenge Punto
1 I’d say that I have covered why that term is NOT substantial.
So the answer is that UCA it does not (substantively) vary with RRPM, which is the point
2 If someone contends that it does vary with RRPM THEY should qualify it, and we’ll see if it is substantive or irrelevant.
Sorry if I did not answer anyone’s important point. “the pig is getting tired"