CP and PNR calculation

[downwind]

Guys,

What is the best way to calculate a CP and PNR not for an exam , but for real life flying! also a way to calc a CP/PNR inflight aswell. That is simple.

[Tree]

Flight time X G/S home
G/S out + G/S home

[Highlander744]

Endurance ( time ) x G/S Home
TAS x 2

Endurance 'should' include some buffer for you to hold at destination.

G/S OUT + G/S HOME = TAS x 2

eg. :

Total fuel endurance overhead or abeam to yr return airport = 3 hrs 25 mins.

If TAS = 300 Kts and W/C = + 35 Kts (ie 35 Kts tailwind component)

Then I would calculate PNR as ( with 1 hour hold buffer at return airport ) :

2hrs 25 mins x 265 =
300 x 2



2.42 x 265 =
600


1.07 Hrs. = 1 Hrs 5 Mins from your check-point.

Hope it helps.

[AerocatS2A]

G/S OUT + G/S HOME = TAS x 2
This is only true when the wind out is the same as the wind back.

If you're working out a PNR based on abnormal ops then your flight level home may be quite different to your flight level out. In that case the winds may be different and you need to use G/S OUT + G/S HOME instead of TAS x 2.

Distance to CP is the same formula except you use DISTANCE instead of time, and the answer is a distance.

CP = Total distance x GS HOME
........G/S OUT + G/S HOME

You may have noticed that these formulas are the same as for an exam. There is a reason they are in the exam!

[Pugilistic Animus]

Downwind,
when it comes to flight planning calculations such as this it is perhaps best to consider the equations in the context of the problem.

What do you want to do?

You want to know whether or not [under various conditions of wind and airplane configuration OEI and OEI/depressurized] how long can I fly before I cannot possibly make it back to my origin? [at least fuel wise]

The specific answer to that question would be a function of how fast you're going over the ground---however you determine that.
how much fuel are you carrying and burning i.e endurance---however you determine that.

Now, take a look at the equation above and see that if you peel away the layers [GS from wind component {plus all of those tedious compass corrections} TAS from EAS and all the AFM/POH data etc.] as required. However, in spite of these complications, the relationship that evolves is actually a very simple one the simplest in fact as alluded above, and an E6B [there's no teaching or learning value in electronic flight computers, what do they ever elucidate about altimetry?!!] and a few hours of play makes these calculations a little fun:8

My response is NOT meant to seem sarcastic or condescending I've seen the Aussie ATPL material!!!, but sometimes because of the nature of aviation and pilot training which is supposed to be soooo difficult:hmm: ...

We can lose the simplicity and freedom of aviation but with time and some cognitive reprogramming we regain a clear view again. But, remember you're totally professional from the moment you soloed in command of a Cub as this is never really a hobby, now that the trauma of your examination(s)! is over... You may again rejoin your mind with the simplicity of [Airplane] flight and now enjoy the true to life esoterica of aviation like the kinematic viscosity of the atmosphere and NACA airfoils, Good Luck!!!

[Pugilistic Animus]

Also, take a look at the units and see [in this case whether or not "time is on your side"]

Engineers and Scientists call this meandering process 'dimensional analysis', pilots call it figgerin'...

[FRQ Charlie Bravo]

For the sake of people looking for a simple answer I'm going to make this easy.

If it's a simple calculation between two points (i.e. no other alternate):

PNR = (Flight Fuel - Extra Fuel Burnt on Climb) / (SGR Home + SGR Continue)

Dist to CP = (Total Distance x GS Return) / (GS Home + GS Continue)
If you have the memory of a sieve (like me) then for data dumping in the first few minutes of your exam these can be written in shorthand:


PNR = (FF-Climb) / SGR Sum

and

To CP = (Tot Dist x GS Ret) / GS SumGo forth and aviate,

[Da-20 monkey]

For the the exams I used to remember it like this:

PET: remember DHOH! (Homer Simpson quote)

Distance x gs Home / (gs Out + gs Home)

and for PSR: THEOH (someones name)

Time to psr = gs Home x safe Endurance/ (gs Out+ gs Home)

others said that (FF-Climb) would be a better definition for safe endurance, but it doesn't have an E in it.:8

[keith williams]

Dist to CP = (Total Distance - GS Return) / (GS Home + GS Continue)


If distance is in nm and speeds are in nm/hour we get the following units.

(A nm - B nm/hour) / (C nm/hour) = A hours - B/C

This will yield an answer in hours minus a number (A hours - B/C).


It will not yield a distance. :ooh:

[4dogs]

Hey Keith,

My reference to dimensional analysis was intended to allow some time for recovery... now you've done all of the work!

Stay Alive,

[Checkboard]

some methods for calculating inflight Critical Points (CPs)/Points of No Return (PNRs) (for on-track work) and Equi-Time Points (ETPs) and Last Points of Safe Diversion (LPSDs) (for off-track work) that are reasonably cockpit friendly?

ETP:

Take your map (that piece of paper that hides at the bottom of your nav bag, under last month's Playboy ®) and fold it so that the two airports you are considering are placed directly on top of each other. Crease the fold line between the two airports and open up the map.

The crease line is the perpendicular bisector between the two airports. (I made that term up , it means that it is half-way between the airports, and at right angles to them)

Any point on this line forms an isosceles triangle with the two airports, (An isosceles triangle is any triangle having two equal sides.) and is a nil wind ETP. Of course the point we are interested in is the place where the crease line crosses our track. This all takes about two seconds to do.

How to adjust for wind? The fastest way I know is to use the GPS/FMS in the cockpit. Set up a point on track at the nil wind ETP, then eye ball the wind vector. Consider the effect that the wind will have flying to each airport (i.e. if it is all cross-wind to ariport 'A' but all head wind to airport 'B', then you will have to slide the ETP along track so as to make the flight to 'B' shorter than that to 'A') I can usually find the actual ETP in about 60 seconds this way. You can even include this point in the GPS flight plan, and have the GPS tell you when you have passed it.

Don't have a GPS/FMS? (Hold on for the maths bit ) find the nil-wind ETP as above, calculate the time to either airport, nil-wind. Multiply that time by the wind (ie time of an hour and a half, wind of 30 knots = 45 nm) Now draw the adjusted wind vector so that the head of the vector is where the crease line crosses the half way point between the two airports under consideration.

Project the vector onto the line between the two ariports. (ouch! what does that mean?) It means take the cosine of the angle between the wind vector and the track between the two airports and multiply it by the length of the vector. (phew!) Not following - forget it then, you don't need to do this and you really need to be comfortable with trigonometry for this method. Now move the "perpendicular bisector" point along the line between the two airports the same distance as the projection, and draw a new "crease" up to your track - this is a pretty good approximation, within a couple of miles, of the actual ETP. (that's right, after all THAT it's only an approximation, which is why I said to "forget it" before )

To adjust further you will need to go into trial and error adjustments as per the GPS/FMS, and that is actually just about as fast if you didn't (want to) follow the trig stuff above. I can usually get an actual ETP in about 2 minutes (by which time the aircraft has travelled further than the adjustment! )

So what's the big deal about ETPs? Well, with the map thingy (takes about two seconds remember) you get a fast approximation, and sometimes (vary rarely) you need to work fast. Also if you have planned enough fuel to your destination then the LPSD is always PAST the ETP, if one of the airports being considered for the ETP is your destination, of course. So you also get an idea of where your LPSD is, or at least how much time you have to calculate it.

LPSD:

Calculate the fuel available for the LPSD. (i.e. Fuel on board minus fixed reserve minus holding minus variable reserve (÷1.1) minus approach allowance)

Calculate the fuel required to fly all the way to the destination (in the configuration you are considering) then to the diversion you are considering.

Now, Fuel available for LPSD ÷ fuel required = dist to LPSD ÷ distance to destination. (Well... almost! )

So divide fuel available by the fuel required, then multiply that by the distance to your destination. This will give you an approximate (within 5%) distance to the LPSD.

To correct it plot this position, calculate the actual fuel to LPSD, then to diversion and compare it to the fuel available. If it is a little high (how many miles will this XS fuel require?), move the LPSD towards you enough to reduce the total track miles by an amount that would save the XS fuel, and check (or vice vesa). I can find the actual LPSD in about 90 seconds this way. Including this point in the GPS plan will have the GPS tell you when you have passed it.

Some more here:

http://www.pprune.org/tech-log/9934-pnr-usage.html

[FRQ Charlie Bravo]

No 4dogs,

Damnit, you have got me. That is not what I meant and I'll change the post accordingly. I only meant to make things simple then I put a "-" where I should have put an "x" and confused things more.

[4dogs]

fixed...

Stay Alive,

[FRQ Charlie Bravo]

This will yield an answer in hours minus a number (A hours - B/C).

It will not yield a distance

Keith, I have corrected my CP formula (I had a "-" where I should have had an "x"). Hopefully this gets rid of the confusion of having a denominator in nm/hr (i.e. the hr unit) but that fraction shouldn't matter as the number will still be correct (i.e. nm/hr is always expressed as nm per (1) hour and anything divided by 1 is going to equal the numerator although technically yes there is another dimension added to the mix). If we stick with the convention of using knots (which shows no fractions other then the assumed 'per nm') the formula will yield a distance.

This thread is incredibly convoluted for a very very simply matter. The formulae below are correct:


PNR = (Flight Fuel - Extra Fuel Burnt on Climb) / (SGR Home + SGR Continue)

Dist to CP = (Total Distance - GS Return) / (GS Home + GS Continue)


Nil wind example (TAS = 250 knots, Distance 500 nm)

Dist to CP = (500 nm x 250 knots) / (250 knots + 250 knots) = 250 nm


Head wind example (TAS = 250 knots, Distance 500 nm, Headwind 25 knots)

Dist to CP = (500 nm x 275 knots) / (275 knots + 225 knots) = 275 nm


Tail wind example (TAS = 250 knots, Distance 500 nm, Tailwind 25 knots)

Dist to CP = (500 nm x 225 knots) / (225 knots + 275 knots) = 225 nm

For those playing the game in Aus have a look at this post (http://www.pprune.org/dg-p-general-aviation-questions/409508-atpl-air-law-tabbing-2.html#post5596951) which gives a way to extract the formula from the ATPL texts allowed in the exams (ie the 727 manual). (That, by the way is why I chose the wording I chose such as "home" and "return" which are, of course, intended to be the same thing.)

I like "DHOH" and will look at making the transition. :ok:

[keith williams]

If you look at your most recent post I think that you will see that you have repeated your error of putting a " -" in place of an " x " (in the blue quotation box).

You have then used the correct signs in your worked example.

[Capn Bloggs]

I bet he hates it when he does that over and over again! :ouch:

http://www.smilies.our-local.co.uk/index_files/doh3.gif

PNR = (Flight Fuel - Extra Fuel Burnt on Climb) / (SGR Home + SGR Continue)

That works fine on the ground but after you're airborne, pick a point eg current position, note fuel and distance from Home and run your PNR forward from that point, reducing your "Flight Fuel"/Safe Endurance by the fuel you need to get from your current position back to home, minus any fuel you save on the descent.

[keith williams]

Yes, I seem to do it more and more as I get older.

I usually find that screaming "BUGGER" makes me feel better........but it sometimes draws startled looks from the people around me.