Critical Point/Point of No Return

- Dag Hammarskjold -

On every flight there are a couple important and often neglected positions and times a pilot might choose to have clear in his or her mind: the Critical Point (CP) and the Point of No Return (PNR). The CP occurs at the moment when flight time to destination and the flight time back to base are the same; the PNR occurs when we will have just sufficient fuel to return to base.

On most hundred dollar hamburger or training flights, the CP and the PNR are not very significant; we normally have more than sufficient fuel and range to accomplish our flight, enjoy our meal or training session and make it safely back to home base. On longer, cross country flights, however, it might be an excellent plan to have a clear idea of where that CP or PNR will occur so decisions can be made in a timely fashion to prevent interesting but unwanted consequences.

When flying in no wind conditions along a straight track, calculating our CP and PNR positions is not particularly difficult. We can load our required fuel plus reserve, take off and fly toward our destination along our track knowing, as long as we do not proceed beyond the half way point, we should be able to make it back to home base safely with our reserve still sitting in the tanks.

Rarely, however, do we fly under such precise, laboratory conditions. We may encounter wind, turbulence or vertical air movement. Our track may not lie along a straight line. Our aircraft may be loaded with its centre of gravity more forward than ideal. We may not be flying a new, clean, freshly polished aircraft. The aircraft may have the odd dent or imperfection on its leading edges or skin. We may have picked up some number of splattered bugs on the leading edges, windscreen, landing gear and cowling. We may encounter an engine malfunction that reduces available power resulting in reduced airspeed.

In my experience, perfection is a rare thing on this planet. If we are pushing anywhere near the edges of our performance envelope, it’s an excellent plan to err on the side of safety rather than trust to hope and wishful thinking.

During private pilot training, most of us were trotted through the lesson called “Range and Endurance.” It is a lesson normally conducted during the early phases of training and may not have been given the emphasis it deserves. During those early phases of flight training many students, I was certainly one, lack the flight or technical experience to fully appreciate or understand the important concepts involved.

One of the basic ideas many of us will have retained from the lesson, however, is that to achieve maximum range with an aircraft we will have to fly at reduced speed. With most light aircraft, normal cruise is achieved within the 55% - 75% power range. The actual RPM setting can be obtained from your POH and is dependent on pressure altitude and temperature.

For most flights there is very little if any benefit to operating at reduced power; the cost saving in fuel is quickly overtaken by the increased flight time and all the costs involved in maintenance. The nice people who manufacture Lycoming engines recommend 65% power for cruise to maximize engine longevity. Commercial operators will almost always run their aircraft at the high end of normal cruise power saving both time and money.

 If it becomes necessary to maximize our potential range, however, a reduced power setting is the way to go. A look at the range profile graph in your aircraft’s POH will give you some excellent guidance. For most light aircraft, operating in the 45% - 55% power range for the given pressure altitude and temperature combined with correct leaning will be suggested to maximize the distance you can fly.

On any given day, the aircraft’s range performance will be affected by a number of factors including: altitude, temperature, weight, centre of gravity location, wind, turbulence and the condition of the machine. Remember those splattered bugs?

Without beating these factors into the ground, a higher altitude will improve range: true airspeed increases by approximately 2% per thousand feet due to reduced parasite drag. A lighter aircraft will have increased range due to a reduction in induced drag: lower weight requires a lower angle of attack at any given airspeed or power setting. An aft centre of gravity will improve range; headwind will reduce range; turbulence will reduce range and a dirty, dented, bug spattered machine will have less range than its cleaner, better kept sister. Proper leaning procedures will also increase range, often significantly. Many light aircraft are not equipped with EGT or CHT gauges, so leaning for best power is often suggested: lean the engine until maximum RPM is achieved. If your machine is equipped with gauges for monitoring exhaust gas and cylinder head temperatures, leaning for best economy becomes more practical and the risk of running the engine too lean and causing damage is minimized.

So, let’s come back to our original question: how do we determine our Critical Point, the point at which it is just as quick and economical to carry on rather than attempt to return to base on a given flight and how do we determine our Point of No Return?

Let’s imagine my friend and I decide to fly a C-172 from my home base at Pitt Meadows, BC (CYPK) to beautiful Lethbridge, Alberta (CYXD) a direct-line distance of 388 NM. We would like to spend one night in Lethbridge so we are rested for the return flight. We will have to carry some baggage as well as the required survival equipment and supplies. With two people, baggage and survival equipment aboard, we can take off with full fuel under gross weight. We won’t be carrying oxygen, so we will need to stay at 10,000’ or below. We may have to do a little dodging around some of the higher peaks as we cross the Rockies; that might add a few extra miles to the trip. We’ll call it a total of 400 NM.

We consult the C-172 POH and determine, at 75% power, we should be able to climb to 9500’ and fly 456 NM with a reserve of 45 minutes at 45% power. We only need to fly 400 NM, god willing and the creek don’t rise. Good to go. Comes the day of the flight and, after obtaining a good flight briefing from FSS and consulting the upper wind charts we find we will have a bit of tailwind, typical for a flight from West to East. We see at 9500’ our average tailwind will be 30 Kts (1). We should be in good shape. That extra help from the wind should make the trip easy and save some time. Just to be on the safe side and for the fun of it, we decide to calculate our CP and PNR. We pull out our trusty copy of From the Ground Up and find the correct formulas: for Critical Point we use the formula P = (D x H) / (O + H) (2). To find our time to turn around, we use the formula: Time = P/G. For these formulas, P is the critical point; D is the total distance to fly; O is reduced ground speed outbound; H is reduced groundspeed home; and G is the groundspeed outbound. Let’s plug in our numbers and see how it all looks.

To mitigate the effects of wind on the return flight, we might want to increase our reduced return speed somewhat. The Rule of Thumb is to increase the best range speed by 10% to reduce exposure time. So, to keep the math simple, we’ll say our return ground speed at reduced power will be 80 Kts. Using our handy formula we determine our Critical Point is 150 NM from home base and the time to make a decision to return to home base must be made no later 1 hour into the flight (3). If our aircraft isn’t new, or hasn’t had its new paint job washed and polished recently, we might want to revise that 150 NM and 1 hour down a touch, just to be on the safe side (4).

Let’s see what happens when we compute our PNR, the point beyond which we will not have sufficient fuel to return to base. Perhaps, not such an important number for this flight, but if we were flying out over water or in the far north where alternates are few and far between, it might become very useful information.

With full fuel at 75% power, according to the endurance chart in the POH, we will have just a touch more than 4 hours flight time, not counting reserve. We can say our time out plus our time back must be less than or equal to 4 hours and work from there. Remembering that speed times time equals distance and distance outbound must equal distance back to base, we can set up a simple equation: speed outbound times time outbound is equal to speed inbound times time inbound. Using the same TAS, 120 Kts., for both legs of the trip: [150t = 90(4 – t)].

Time outbound is 1.5 hours, one hour and 30 minutes. Time for return is 2.5 hours, two hours and 30 minutes. To have sufficient fuel to return to base, we must turn around at or before 1.5 hours into the flight, approximately 225 NM from home base. Reducing speed for the return journey will give us a bit more range, but let’s not put too fine a point on the problem. A bit of extra fuel to cover contingencies is all to the good. Landing with nothing more than minimal reserve sloshing in the tanks is not a stress reducing experience.

Everything looks good, however. We appear to have sufficient fuel to make the trip in one hop with extra to spare; there are several alternate destinations enroute and we know when and where we are actually half way in terms of distance and flight time so we can make the decision to return home, if required.

We did discover an interesting fact, however: hanging on to the assumption that half way is half way could have put us in an awkward position. Under the conditions described, it turns out we actually have a fairly short period of time in which to make the decision whether or not we can return to home base. Half way in terms of distance isn’t necessarily half way in terms of time. The delightful tailwind that will provide us so much help toward our destination all of a sudden becomes quite a barrier to our return home and our decision to return, if required, must be made fairly early into the trip.

Many pilots enjoy taking long cross country flights. It’s a great way to see the country and experience the joys of flight. It is a good idea, however, to be clear about both our potentials and our limitations so we can make informed and intelligent decisions and continue to experience the joys of flight, keeping our stress levels and our unexpected and unplanned adventures to a minimum.

Enjoy.

Notes:

1. Just to keep the math simple, we’ll assume a constant wind direction and strength and a straight-line track. With more realistic conditions, we might expect winds with some degree of cross-track component both outbound and on return and would have to factor them into our calculations.

2. This formula is often applied to calculate the Critical Point for twin engine aircraft in the event an engine is lost and the machine must return to base at reduced airspeed, approximately 60% of normal cruise speed. It can also be applied toward the single engine aeroplane scenario when reduced airspeed is used to increase range or reduced airspeed results from other possible reasons: i.e. magneto failure or other malfunctions that may produce reduced speed.

3. P = (D x H) / (O + H). In our case P = (400 x 80) / (133 + 80) = 150.23 NM. Time is P/G or 150.23/150 = 1.0015 hrs., one hour and .09 minutes.

4. If we stick to our original cruise power setting, giving us 120 Kts TAS both ways, we find that P = (400 x 90) / (150 + 90) = 150.00 NM. Time = 150/150 = 1 hour. Pretty much the same conclusion: if we fly past our Critical Point, 150 NM, considerably less than half way in terms of distance, it becomes a longer trip back to our home base than it would be to continue to our original destination. The only benefit we derive from reducing airspeed and power for the return flight is fuel savings.