depending on what comes after this, I may add more,...looking at that relevant section of the airplne flying handbook, I see the example given is not very encouraging: so I decided to place a more encouraging example but assuming no rwy gradient and no wind but first let me post some figures-:
at 65 KTAS turn radius [feet] at a bank angle[phi]=TuR[phi]
so 1030
feet [20deg] etc 649 [30], 375 [45], 216 [60],
at 75 KTAS:
1372 [20], 865 [30], 500[ 45], 288 [60]
turn rate [deg/sec] [bank angle]
at 65 KTAS:
6.1[20], 9.6 [30,] 16.7 [45], 29 [60]
at 75 [KTAS]
5.2 [20], 8.3 [30], 14.54 [45], 25 [60]
using many aerodynamic assumptions and assuming a 'perfect 180' not a 'pseudo-procedure turn' lets check out a reasonable example aumming vy=v glide and Vx = 65 KTAS all in a standard atmosphere,...
I'll use Vx so that you'll be closer after an engine failure
assuming a 500'/min climb rate and an engine failure occurs 2 minutes after takeoff from 1000' feet,...then immediate recognition,...since 500 feet per min = 470'/nm 65 knots [according to my E6B] you are 2.12 miles away now let say acceleration to Vglide [since there's be no zoom reserves here you lose 100' in accelerating and traveled a negligible distance,...a perfect 180 degree turn at 30 bank from 75 KTAS = has a radius 865' and a rate of 8.3 deg sec so 180 deg takes 21/sec at a ROD of 800'min that =21/60=.35 min so a 400' loss +100 from acceleration at 75 knots and lets add 30 seconds for good measure so you've been decending, lost 400' + 100' so 500' lost in the turn around + 400 feet for error so you've lost 900 feet 1.21 minutes at 75knots you travel 1.25 nm /min and you still have about a mile to go
see not good!!!
because, this is PPRuNE and that's the Airplane flying Handbook,...And I'm
Pugilistic Animus