Good day everyone!

old student of mine msg me asking me about PNR, stating they've been getting conflicting info. I explained and turns out information they are receiving from different sources tell 2 different stories

My explanation: Regarding what happens to PNR with changes in wind.
According to formula you always shortern distance to PNR with any wind.
ex.
calm wind conditions
endurance 10 hours, Ground speed: 100 knots

according to formula
(Endurance x groundspeed out x groundspeed home) / groundspeed out + groundspeed home

therefore 10 x 100 x 100 / 100 + 100 = 500 nm

and with 50 knots of headwind you get
endurance 10 hours, groundspeed out: 50 knots groundspeed home: 150 knots

therefore 10 x 50 x 150 / 150 + 50 = 375 nm

and finally with 50 knots of tailwind:
endurance 10 hours groundspeed out: 150 knots groundspeed home:50 knots

therefore 10 x 150 x 50 / 150 + 50 = 375nm


just by that fact it should prove that PNR will move closer to the departure airport with ANY wind condition compared to calm wind.

According to ., or aerocourse (cant remember which now), they are claiming that it takes longer to get to PNR in a headwind, and less time to get to PNR in tailwind, therefore PNR always move into the wind.
As above, unless I'm making a mistake in calculations, how is a creditable book able to make such a big error in something they are teaching? I don't know what addition she has but I sure hope this is an old book and this mistake has been fixed!
if anyone can see issues with my work. please pipe up!

On the iPhone here so I haven't taken the time to do the explicit math, but if you think about it in logic, I'd go with the statement that you make at the end.

If you travel to the point of no return in a headwind, you are burning fuel/hr, and you make it to a point, x, (which would be less than in a no-wind situation). Now, when it's time to return, your headwind turns into a tailwind, and you can return quicker, (ie. your outbound leg will be longer than your return leg).

If you reverse this situation, your point of no return is achieved quicker, because on the return (inbound) leg, you will take longer because your tailwind has no become a headwind.

I'd go with ... and aerocourse on this one.

Point of No Return Distance = Time out x Groundspeed out = Time back x Groundspeed back = (Endurance - Time out) x Groundspeed back

TO x (AirSpeed-HeadWind) = (E-TO) x (AS+HW)
TO AS - TO HW = E (AS+HW) - TO AS - TO HW
2 TO AS = E (AS + HW)
TO=E(AS+HW)/2AS
PNR = TO (AS-HW)=E(AS+HW)(AS-HW)/2AS

PNR=Endurance(AirSpeed²-Headwind²)/2AirSpeed

Unless my math is wrong (which at this time of the day could very well be) the stronger the headwind, the smaller the PNR.

scavers wrote: If you travel to the point of no return in a headwind, you are burning fuel/hr, and you make it to a point, x, (which would be less than in a no-wind situation). Now, when it's time to return, your headwind turns into a tailwind, and you can return quicker, (ie. your outbound leg will be longer than your return leg).

If you reverse this situation, your point of no return is achieved quicker, because on the return (inbound) leg, you will take longer because your tailwind has no become a headwind.

+1

This is my understanding of PNR as well. I wrote the IATRA about a month ago and had no problems with the PNR question using this logic (and the equation provided). But who knows, may have been luck!

Heh. I WAS tired after all.

My equation is right. But it would be just as right if I had used Tailwind instead of Headwind.

So the stronger ANY WIND is, the closer the Endurance-based PNR is. Which makes sense and I agree with DH772 : if you turn back overall you have two legs to fly, one with a tailwind, one with a headwind. What leg is first flown is irrelevant.

Now, what is called "PNR" : is it the furthest point where you can turn back safely based on your endurance?

Or is it the furthest point where turning back is more economical than proceeding towards destination? This could be a "point of no return" as well : if you have a problem beyond that point, keep going to your destination, you'll reach it sooner than your departure point if you turn back.

Based on the answers from the aforementioned workbooks, it's probably the latter. Whereas DH772 talks about an endurance-based one.

gaamin wrote:Heh. I WAS tired after all.

My equation is right. But it would be just as right if I had used Tailwind instead of Headwind.

So the stronger ANY WIND is, the closer the Endurance-based PNR is. Which makes sense and I agree with DH772 : if you turn back overall you have two legs to fly, one with a tailwind, one with a headwind. What leg is first flown is irrelevant.

Now, what is called "PNR" : is it the furthest point where you can turn back safely based on your endurance?

Or is it the furthest point where turning back is more economical than proceeding towards destination? This could be a "point of no return" as well : if you have a problem beyond that point, keep going to your destination, you'll reach it sooner than your departure point if you turn back.

Based on the answers from the aforementioned workbooks, it's probably the latter. Whereas DH772 talks about an endurance-based one.

Wouldnt that be the "Critical Point"?

The general formula used to calculate the distance of a CP/ETP from an Alternate is:
Distance to CP = Distance (Alt to Dest) x Groundspeed to Alt ÷ (Groundspeed to Dest + Groundspeed to Alternate)


The general formula used to calculate the distance to the PNR from the Alternate is:
Distance to PNR = Flight Fuel Available (Alternate to Destination) ÷ (SFF (To Destination) + SFF (To Alternate))

edit: notice the double brackets? make sure you do the operations in order

Wouldnt that be the "Critical Point"?

The general formula used to calculate the distance of a CP/ETP from an Alternate is:
Distance to CP = Distance (Alt to Dest) x Groundspeed to Alt ÷ (Groundspeed to Dest + Groundspeed to Alternate)

The general formula used to calculate the distance to the PNR from the Alternate is:
Distance to PNR = Flight Fuel Available (Alternate to Destination) ÷ (SFF (To Destination) + SFF (To Alternate))

edit: notice the double brackets? make sure you do the operations in order

Indeed, yea CP is point which it takes say time to go either back to destination or continue you. And using that formula it DOES move into the wind. So tail wind, it will be closer to departure and headwind closer to destination.

Back to PNR though, I understand the logic that you have tailwind, you get there sooner but obviously the formula tells a different story. And as someone mentioned above, either way you'll be flying both legs, (aka a headwind and a tailwind) so yea I guess it CAN only move closer to departure because you will always be fighting with a headwind and tailwind!

Ok thanks everyone, sticking with original thoughts here about PNR. Just didn't want to be teaching someone false information and telling them a book is wrong without having all details.

When flying long distance over ocean flights how much faith would you put into using these formulas to determine not only the point of no return but your reserve fuel?

PNR is the point at which you will NOT make it back home if you turn back because you will not have enough FUEL (ie: the POINT at which you canNOt RETURN home, makes sense eh...). It can never be more than 1/2 the max endurance range. To be safe, calculate it with your normal cruise range. It doesn't take an aerospace engineering degree to figure out that ANY winds will bring this closer to departure point. (you you have a tailwind on departure, you will need to fight the headwind on the way back to departure point and vice versa).

The CP is the point at which it will take the same TIME to go destination or go back to departure point.

Both forumlas are based on constant winds, obviously and are normally only used as an estimate to give you an idea. Live (in-cockpit) analysis is always required to know what your options are.