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