how to solve ? 2

[ARGPILOT]

distance A to B 2346 nm
GS out 365
GS back 480
safe endurance 8.5 hrs

the time from point A to the point of safe return (PSR) A is ?


thanks

[Seat1APlease]

If you're coming back then the distance between A and B is largely irrelevant.
distance =speed*time, so
ground speed out *time out=ground speed back*time back, since the distance is the same both ways, and since time back is (8.5-time out) then:-
365*To=480*(8.5-To)
This is basic secondary school maths, you're going to struggle with other parts of the course, or are we doing your homework for you?

[ARGPILOT]

i am sorry but i am looking for a formula

like the one for PET (point of equal time) which is

PET = Distance * (GS back/ GS out + GS back)

[Farmer 1]

The basic equation for Point of No Return (never heard of PSR before) is:


Distance to PNR = (Endurance in hours x gs out x gs home)/gs out + gs home


This is to tanks empty, so you need to reduce the endurance by any reserves you feel you need.

[Capt. Slow]

Isnt the equation:

time/endurance = Time home/(time outbound+time home)

or

T/E=H/(O+H)

? (always get the O & H's muddled)

so that would give a PSR of 289.7mins or 4.8 hrs

To use the equation just work out the right side first then multiply by the bottom part of the left side (endurance)

Finished ATPL's this year but its all startin to get a bit hazy...

[ARGPILOT]

thanks farmer

[pilotmike]

ARGPILOT, Farmer 1 was incorrect when he wrote

Distance to PNR = (Endurance in hours x gs out x gs home)/gs out + gs home


as this simplifies to endurance x gs home + gs home - which is incorrect.

The solution you asked for is 4 hours, 49 minutes and a fraction over 42 seconds (assuming an infinitely quick turn back) to arrive back with dry tanks.

Seat1APlease's advice was spot on, including the correct formula, leaving you the (simple) task of 'gathering terms'. Capt. Slow's version was also correct, with the correct answer.

It seems somewhat odd that you should thank the one contributor who 'told you wrong', yet you managed to miss the two correct solutions which were given to you.

PM

[Farmer 1]

Funnily enough, Pilotmike, that is presactly the answer I get using my quoted equation.

I wonder if you are confused by my not enclosing the bottom line of the equation in brackets, i.e. (gs out + gs home).

I was trying to keep things as simple as possible, and I thought writing it like that might complicate the issue. I am assuming that you thought I thought the gs home on the bottom line should be added to the result of the rest of the equation, but that is impossible because you would be adding speed to a distance.

My equation is correct, and in my opinion the simplest to use. However, that's only my opinion.

[Farmer 1]

Right, I'll try again.

I have tried to lay out the equation as it would be written, but could not get the system to work how I wanted.

So, in longhand: first, add gs out to gs home. Call the result gs mean.

Multiply the endurance (in hours) by the gs out, then multiply that result by the gs home. Then divide the result of that by gs mean.

The result is the distance to the PNR, from which you can find the time to PNR should you so wish.


To make my original effort mathematically correct, it should have been thus:

Distance to PNR = (Endurance x gs out x gs home)/(gs out + gs home)

Looking at it now, it's obvious that my original post did not make things any simpler, which was my intention. What's that about paving the road to Hell?

[ARGPILOT]

pilotmike

thanks for the contribution to the post,

reason why I thanked farmer1 is because he tried to help me, he gave his opinion, even if he gave me a wrong answer, I still thank him.

as far as the equation, I dont think it makes a different the ( ) on the final result

thanks to everyone