View Full Version : Equal Time point with off route Alternates - How?
Greeny989
15th Oct 2010, 07:02
The basics I have:
Flying from point A to point B, where is the equal time point to return to A or continue to point B?
I can do that in still air and with wind using the formula:
Dist to ETP = (total Dist X GS Home) divided by (GS out + GS Home)
Where I am having problems and can’t find the information is
Flying from point A to point B, where is the equal time point to return to A or divert to the off route alternate at point C or what is the equal time point to 2 different off route alternates C & D when flying along route A to B. How do I do this and account for wind?
Is there a way of working this into the above formula or does it need to be done via plotting and if so how?
Any help would be greatly appreciated
Thanks
Greeny
Greeny,
it depends on where the wind is coming from, and where the airports C & D are in relation to A and B. So no, it can't be done without using at least a bit of trigonometry.
PBL
Greeny - it is best done by 'puter - normally a flight planning programme is used. If you are trying to 'fag packet' it, good luck! Essentially it is a series of iterations for successive points, at each one of which your 'GS out' and 'GS back' change due to wind changes. I guess you could write a spreadsheet construct to help, but ...............:eek::eek::eek: You would need to stick a pin somewhere 'sensible' on your route (ie start with the still air ETP and move it a sensible bit along/back on track just eye-balling the wind chart) and work along and back to see what happens to flight times as you move it.
What is your actual need? It can happen in flight with a re-route and then, well, you just do it to the best of your ability.:) We do not carry the software (yet) to enable a new ETP structure to be made in flight.
Checkboard
15th Oct 2010, 08:46
If you are trying to 'fag packet' it, good luck!
... or you could follow some of my methods below ;)
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: By hand, the old fashioned way :8
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? Mark your 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') Make a quick [distance/ground speed] check for each leg, and adjust if the times are a bit out. I can usually find the actual ETP in about 60 seconds this way.
Want to be more accurate? (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 a nil-wind time of an hour and a half, a forcast wind of 30 knots = 45 nm 'adjusted' wind vector.) Now draw the adjusted wind vector on the map, so that the head of the vector is where the crease line crosses the half way point between the two airports under consideration (the nil-wind ETP).
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, 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! )
ETP: By FMC, a newer fashioned way :8
The fastest way I know is to use the GPS/FMS in the cockpit. You can even include this point in the GPS flight plan, and have the GPS tell you when you have passed it.
You can't fold the electronic map display ion the flight deck, so use the fix page to place a fix at each airport you are interested in. Draw a circle around each airport big enough to overlap each other (both circles must be the smae size). The two points of overlap form two points on the perpendicular bisector line - the crease in the map - above. With a bit of trial and error, you can adjust the size of the circles until the intersection is over your track, then pick up that point (the nil wind ETP) on the fix page, and place it into your flight plan at the appropriate point. You can then temporarily place each airport in turn after that ETP point to check the time to each airport - and if necessary adjust the point back and forth along track until the times are exactly the same (i.e. using the FMC to calculate adjustments for wind effect)
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: Last point of safe diversion to an off-track airport
Calculate the fuel available for the LPSD. (i.e. Fuel on board minus fixed reserve minus holding minus variable reserve (÷1.1 for 10%, ÷1.05 for 5%) 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] ÷ [total fuel required] = [dist to LPSD] ÷ [distance to destination.] (Well... almost! ).
This means that the distance along track to your diversion point is roughly the same percentage of the total distance as the percentage of fuel available is compared to the fuel required to fly all the way to the destination and then divert.
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.
As an aside:
For you piston guys, in the Australian regs there used to be a requirement for twin aircraft to ensure that they have enough fuel to fly (on two engines) to the single engine CP and then fly one engine out to an airport.
I don't know off the top of my head if this requirement survived the "just don't run out of fuel - OK?" changes where the CAA decided to get fuel reserves etc included in Company Ops manuals (of which maybe 10% have been ammended after 5 odd years, I bet...) however as most pilots learnt CPs at CPL stage, and that was, pehaps, two - three years before they really started flying twins, I bet that hardly anybody does this.
Of course the whole situation is not helped by the manufacturer's manuals, very few of which (especially Piper's) give any numbers for single engine cruise, but that's another whinge...
So, time for a "Rule of Thumb"
When a piston twin loses an engine, it has to slow form its normal cruise speed (with lots of parasite drag) to close to the long range speed. You will find that the aircraft is flying more efficiently on one motor at the single engine cruise speed, than on two at normal cruise! (but not as efficiently as on two at long range cruise, due to the added drag of the engine out thing.)
So the aircraft will fly furthur (through the air) one one engine than on two! Doesn't work for turbines, as they are forced to operate at a (inefficient) lower altitude.
So, the rule of thumb? If the headwind is less than 25% of the single engine cruise speed, planning normal ops fuel will also cover the engine out case.
So now you can say to the CASA guys when they jump out from behind the fuel bowser - yeah, I planned for that, and proceded to baffle them with the above!
Greeny989
15th Oct 2010, 09:55
Checkboard,
Thank you for your time and effort on your reply, your post covers everything I need. I fly single pilot helicopters so it is for pre planning, but the folded map still air ETP looks easily do-able in flight.
Greeny.
Great bit of work, CB! Origami rules.
JammedStab
15th Oct 2010, 13:55
So, time for a "Rule of Thumb"
When a piston twin loses an engine, it has to slow form its normal cruise speed (with lots of parasite drag) to close to the long range speed. You will find that the aircraft is flying more efficiently on one motor at the single engine cruise speed, than on two at normal cruise! (but not as efficiently as on two at long range cruise, due to the added drag of the engine out thing.)
So the aircraft will fly furthur (through the air) one one engine than on two! Doesn't work for turbines, as they are forced to operate at a (inefficient) lower altitude.
Seem to remember a wriiten procedure from the old days on the Beech 99
where if you were in a situation of not having enough fuel to destination(remote area), you could shut down one engine to extend range. Can anyone cofirm?
Quote:
Originally Posted by Checkboard
So, time for a "Rule of Thumb"
When a piston twin loses an engine, it has to slow form its normal cruise speed (with lots of parasite drag) to close to the long range speed. You will find that the aircraft is flying more efficiently on one motor at the single engine cruise speed, than on two at normal cruise! (but not as efficiently as on two at long range cruise, due to the added drag of the engine out thing.)
So the aircraft will fly furthur (through the air) one one engine than on two! Doesn't work for turbines, as they are forced to operate at a (inefficient) lower altitude.
Seem to remember a wriiten procedure from the old days on the Beech 99
where if you were in a situation of not having enough fuel to destination(remote area), you could shut down one engine to extend range. Can anyone cofirm?
Lets look at these two statements in isolation.
As regards the piston twin...only a few can do as advertised in the quote, the CV440 is one of those that I have flown.
Driftdown is however, a distinct possibility.
As regards the BE99....only at very light weights.
The BE99 wing was was optimized for lower altitudes, as the airplane is unpressurized.
Hmm! Not a lot of use to a helicopter pilot?
In truth, for fixed wing jets, it all depends on the rpm where the max fuel efficiency occurs. In the BAC Lightning it was reckoned that shutting down one put the other into the max efficiency band so you got more out of the tank (as long as you got it relit when the baddies came along:) )