OK, how about comparing 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.
Any other suggestions???
[This message has been edited by Checkboard (edited 15 January 1999).]