An easy guide to fuel planning and cruise performance

[Lukasz]

What did you fly today?

I flew Cessna 172X. Before anyone points out, that there is no such version of popular Skyhawk, I tell you, that in fact it exists. X stands for X-Plane. During additional research needed for this tutorial, I've found that even the best planes depart in some ways from their real life counterparts, in terms of performance. Sometimes the difference is minor, sometimes not. Some of these differences are coincidentally common to every plane I've checked, so it looks like they are caused by X-Plane itself, despite best work done by a plane developer. Others are plane specific.

In terms of basic principles, simulated flight model is very similar to mathematic atmosphere model used in modern weather forecasting. You input starting values, add current direction and rate of change and watch, how the future unfolds, here and now. But there is a catch: you can predict accurate weather for a couple of days, after that simulation model and reality go their own ways. Where should be sun, is raining. It's caused by natural instability of fluids (as air and vapor) as well as inaccuracies in atmospheric data measurement. Wind was reported to be 5 knots, while it was in fact 5,23973456893487 knots. These subtle differences are not visible at first, but they do accumulate with time and change the calculations. There are also limitations as to how much calculations your hardware can perform in a given time. Week-long calculating forecast for another day is pretty much pointless, as running very detailed flight model at 1 frame per second.

Why am I writing this? Because this tutorial involves flight testing and gathering performance data from "our planes", in order to

better understand how do they fly and therefore how to better fly them. Real plane may have stall speed of 80KIAS, while flight testing shows, that out stalls at 84. Now you can do two things: cry that the plane is crap or learn how to properly fly it in a sim, with regards to sim performance, capabilities and limitations. It still can be greatly satisfying, and still you can learn a thing or two, because the exact values may be different, but the concepts and principles are always the same.

Besides a difference between 80 and 84 KIAS is only 5%. I'd say, that the developer did a very good job coming that close. Personally, I've set the the following criteria for plane accuracy: within 5% of original is absolutely fantastic and within 5-10% is very very good. I encourage you to find your own criteria, some of you may want a air temperature forecast accurate down to 5 degrees, while others will be happy with just "warm" or "cold". Developers themselves could also take an advantage out of this, by publishing POHs based on performance data from their planes, so they could show off how much accurate their planes are and we, the pilots, would have the guidelines how to properly fly them.

I also strongly discourage any smart asses out there, who would like to use the methods described below to harm any developer or make him a bad publicity, because "the plane is not accurate". If you do that - it will be the last detailed tutorial from me, and there are few yet to be written. If you really really really feel, that there is something wrong with the plane, gather solid data and write an email or personal message to the dev, with the solution how to possibly fix it. Be polite and don't spam - these are busy men, who deserve our understanding and respect, because without their work we would be flying paper planes at best.

The chart

This tutorial is dedicated to flight and fuel planning with regards to plane's aerodynamic efficiency only. In reality there are other factors influenting choosing of airspeed and altitude, like ATC, weather (icing, buildups, "ride quality" to name a few), airspace constraints and local rules. I'm going not to deal with these additional considerations in this tutorial.

Having said that, let's have a look, how does a plane fly and what we can gather from it.

What you see, is a chart made during level flight. The plane was flown as slow as the autopilot allowed and then I've firewalled the throttle to accelerate to the top speed. The purpose of that was to record aerodynamic and engine performance over practical speed envelope, to establish some key points (speeds), that will be needed for fuel and flight planning. Have you ever wondered, how fast do you need to fly during a climb? Or what is the best speed for cruise? You have all the answers right there, on this chart

Labels explained

While the lines on chart have their labels posted, they require some explanations, before we can move onto more interesting things. I will also use two words: a peak and a downpeak. A peak is the most upper point of a curve, the highest vale recorded. The downpeak (does that word even exist? Neither I know, nor my dictionary...) is the opposite, the lowest point, the lowest value recorded. Also all airspeeds mentioned are indicated airspeeds, unless noted otherwise! Why, will be explained at the right moment.

pwr avlb - power available. That's how much horsepower the engine can generate. Since the throttle was all the way up, power line shows constant maximum value through the entire speed range.

pwr req - power required for level flight at constant speed. That's how much power the engine should produce, to fly the plane at the speed specified below. The faster you go, the more power required, because the engine would have to fight more drag, as the airspeed increases. We know from physics, that drag rises as a square function of airspeed: increase airspeed two times and drag will rise four times. Also the faster you go, the more fuel is burned - more power equals more fuel flow, however fuel flow line on the chart is level, because the engine was at full power all the time.

This curve has one very interesting point on it, the downpeak. It's around the minimal speed at which autopilot was able to fly the plane level, but on other charts I've made it was a nice parabola. This point shows the airspeed, at which there is a minimal power required for level flight, hence the minimal fuel burn. That's the airspeed for maximum endurance. You won't get far flying at that speed, but you will be able to stay in the air for a long time, for example during a holding with minimal fuel reserves on board.

pwr excs - power excess. This is how much power you have "in reserve". It can be used to accelerate the plane or to climb. Add power, while maintaining level flight and the plane will increase its speed. Add power and raise the nose to maintain the airspeed - tha plane will climb at that airspeed.

The peak on this curve, is nothing other than Vy or best climb speed. Climbing at that airspeed will allow you to gain the highest altitude in a given time and it is used during climbs to low altitudes, on short flights or during initial climb during long trips.

thr avlb - thrust available. Ah, now the real fun starts! I really don't know, why people are so much interested in horsepower, while it is the thrust (or torque for cars), which does the real job. Thrust is nothing other than a force, pulling the plane forward, against the drag. This force is produced either by hot exhaust gases coming out of a jet pipe or by the airstream accelerated by a propeller. As you can see on the chart, the faster you fly, the less thrust is available, because the engine can't push the air fast enough, with regards to the ambient airflow caused by plane's movement, because thrust can be seen, as a difference in speeds between accelerated airflow (hot gases or propwash) and ambient air.

For propeller planes, thrust is also linked to propeller's efficiency, which basically means how much engine power is converted into thrust. Prop eff 0,75 means, that only 75% of current power is used to generate thrust, the remaining 25% is used to overcome propeller blade's drag, air compressibility issues as well as other things. Propeller efficiency generally rise with airspeed up to some point, after which it starts to drop, with further airspeed increase. Most propellers have the efficiency between 75-80% for good props and 80-85% for excellent props. We'll need that knowledge later

thr req - thrust required for level flight at constant speed. It's one of the most important things to understand from the chart. Because thrust is the force that directly fights with plane's drag, it's value will be a direct indication whether you're flying the plane at optimal airspeed or fighting the drag too hard, which costs fuel. A lot of fuel actually, as when airspeed increases two times, the drag and thrust required increase four times... Since some of engine's power is "wasted" because of propeller efficiency, you need to produce even more power to compensate for that and fuel flow gauge starts showing some very unnerving values But fear not! There is a solution to that.

Lift-to-Drag

Some of the more advanced "tinkerers" out there may remember, that in Airfoil Maker there is a curve labelled a L/D or lift to drag ratio. That's not the one we'll be dealing with. Instead, we need L/D ratio of the whole plane, because we're flying the plane - not just the wings' airfoils. Plane's overall L/D ratio can be found on one of the data stripes, that can be displayed on screen during flight (like the fps count usually seen on my screenshots, I fly with it and leave it on purpose, as a trademark ).

Lift to drag ratio is a key concept of this tutorial, as every fascinating and useful data we can use to estimate plane's performance comes from or is linked to it. But if it's so much important, than why didn't I include it on the chart? I didn't have to L/D curve is identical to thrust required curve, only turned upside-down. The downpeak of thrust required is the peak of L/D, both of them being very important points of interest, as they indicate an airspeed, at which we need the smallest thrust to fly at a constant altitude. The smallest thrust required means the smallest drag, which in turn means the smallest work required to make the plane fly. And the smaller work, the less fuel burn. Airspeed at which you have the smallest thrust required - OR HIGHEST L/D - is the speed at which the plane is THE MOST EFFICIENT aerodynamically. It's the airspeed, at which the plane can cover the maximum distance for a given fuel load - the best range speed, sometimes called "go far speed" or "slow cruise". Also, should the engine fail (or wasn't installed at all, like in gliders), it's also the best glide speed, which is the airspeed at which you can fly the furthest from your current altitude.

However, there's a little catch For jets this most efficient airspeed is exactly equal to the least thrust required or the highest L/D speed and can be easily obtained from the data stripe. Not so easy for the propeller planes, as we have this wasteful propeller efficiency issue That's why purple "max range" curve is shifted a bit towards higher airspeeds (peak at 104 KIAS), with regards to thrust required curve (downpeak at 95 KIAS). My research has shown, that you can easily estimate the most efficient speed for that case by multiplying best L/D speed by 1,05. It's not absolutely accurate "coefficient", as it can spread from 1,027 to 1,094 on very well designed planes I have used, because it depends on propeller's efficiency, but it's fairly good default to have fairly accurate speeds (difference within 2-5 knots between calculated and actual chart values). Can you fly that precisely anyway?

The other interesting airspeed we can obtain from L/D ratio, is the best cruise speed. Remember, that the faster you fly, the more it will cost you in terms of fuel, but on the other hand who wants to fly so slooooow at best range speed? Sometimes you don't need that range, but there is little time to fly. So, you want the speed, at which the biggest increase in airspeed over best range speed is accompanied by possibly smallest penalty in fuel flow. Such speed is marked by the peak on thin blue curve on my chart (at 138 KIAS) and is called best cruise speed or "go fast speed" or "Carson's speed". You can also estimate it by a simple coefficient (a real life one - I didn't made this one and it actually works for real planes also!). Just take max range speed (the best L/D one or best L/D adjusted for prop efficiency) and multiply it by 1,316.

Let's sum it up!

chart values, all based on test flight:

best L/D - 95

best range - 104

best cruise - 138

calculated values (the same plane and conditions):

best L/D - 95

best range - 95 x 1,05 = 100

best cruise - 100 x 1,316 = 132

Even with the maximum "propeller efficiency adjustment coefficient" of 1,094 for this plane and this conditions, the values obtained from calculations are reasonably close to the actual test flight data and as such can be used during normal everyday flying, all being around 5% difference

Am I crazy? Who would worry about fuel burn in a sim?? A lot of people, actually Have you ever limped back to base in Sturmovik, with fuel tanks punctured? Or have you ever had a dilemma in Xeconomy, whether to take more fuel or more freight, which brings you money? Or have you ever tried to make it to that distant island, without possibility to make a fuel stop over the ocean? Right

By the way, if anyone was interested about thr excs curve on my chart, it's thrust excess value, the peak of which is Vx speed - best climb angle speed. It's used only, when you have to climb as steep as possible, in order to fly over an obstacle like a treeline at the end of short runway or that mountain suddenly protruding from a fog. Do not use it for normal climbs, because the speed is low and thus the airflow cooling the engine and it's easy to overheat it that way. While we're at climbs, there is another climb speed, so called "cruise climb". You'll fly at higher forward airspeed and lower vertical speed, to improve engine cooling, and forward visibility, as well as cover as much ground as possbile during the climb. Take Vy and add to it 15-20 KIAS for regular GA planes or add 30 KIAS for high performance pistons and you'll be fine Jets and turboprops are free to climb at Vy all the way up, provided that turbine limits are observed.

Descends are even easier. In unpressurised planes try not to exceed 500fpm, for passengers' comfort, in pressurised pistons 1000fpm, turboprops and jets can go faster - 1500 and 1800fpm and even more. Fly that vertical speed and set the power to maintain engine and carburetor temperature high enough, to prevent overcooling or carb ice.

Now, with a single test flight and a simple chart, we have uncovered all the speeds that will be needed during flight planning, which eliminates lots of guessing and estimating, as well as enables really efficient plane operation. Well, not really all the speeds, but I'll cover that after the break

It's half past midnight here (I'm writing since 20:00) and I need something with energy in it The title of this song is "Insatiability", quite appropriate when it comes to flying

"The Others"

I understand, that there are other sims and their fans around, who can't just turn on the data stripes and check their L/D ratio. Since I want this tutorial to be as much universal as possible, I've found a way to overcome this. Take your plane into the air, idle the engine (do not turn it off completely) and note the total weight. Now, fly at different airspeeds and watch closely vertical speed indiactor. You may want to fly for a moment at a given forward speed, to let VSI stabilise properly. The IAS that yields the lowest VSI is your best L/D speed. You can calculate best range and best cruise speeds from that point. Vy is around best L/D speed divided by 1,316 (yes, that's the same real life coefficient. In reality now you've calculated best endurance speed, but it's close to Vy, so we can use it here. Better than then nothing. If that annoys you - switch to X-Plane and have professional data stripes ).

Aerodynamic efficiency indicator

Can you tell me the name of an airplane which was equipped with that very useful gauge? Whatever crazy invention came to your mind, you were correct. In fact every known to me plane as well as helicopter and other flying "things" are equipped with it. You may also know it under the designation of airspeed indicator, which in reality tells how the gauge works, but doesn't tell the full story at all! At Vs plane no longer is aerodynamically efficient, which results in a stall and often in loss of control. At Vmax the plane can't be more "efficient" and stops accelerating, unless you perform steep dive, but that can also lead to a massive unefficiency. Fortunately, we have a whole range of airspeeds to choose from, while maintaining a healthy efficiency margin

If you have read my previous tutorial, you may remember that the airspeed indicator is a notorious liar, because of the offset between indicated and true airspeed. That is correct, but only with regards to navigation. For the purposes of controlling the plane, you really want the airspeed indicator to work that way and that's the reason, why the "liars" were not "repaired" so far - modern plans have TAS readout in addition to IAS, not instead of it.

Airspeed indication is created by the force of incoming airflow into the Pitot tube. So is the lift, but in this case it's incoming airflow around the wings. The more incoming air, te more Pitot indication and more lift. The less means the less, to the point where Pitot shows on the gauge stall speed and wings loose last bits of lift. What is important, that it does happen exactly the same way regardless of altitude. The airflow is airflow, it only matters how strong and how fast it is, thin air on hight altitude can be compensated by increase in true airspeed, so that IAS remains the same (there is only one exception from this - takeoff/landing from short runway at high pressure altitude, but I'm not going to hijack my own post into that area right now!). The concept of "aerodynamic efficiency indicator" is important, because you can perform only one test flight and one chart for one altitude and the airspeeds recorded and calculated will be equally valid on other altitudes. Really, there is no need to make a chart for every flight level available for that Learjet

Further down the rabbit hole

But, as you may have already guessed, nothing is as it seems and there is always some catch or another complication, that has to be taken into consideration. Life wouldn't be the same without them, would it?

Let's imagine a plane flying at a constant speed in a level flight. Weather is all the time the same, there are no other variables, that could spoil the balance. With one exception - weight. Plane burns fuel and becomes lighter, as time passes, and it will start to climb, if you left it at previous cruise settings. You can prevent this change in altitude simply by lowering the nose - but that would let the plane to accelerate and fly faster, than optimum airspeed we have calculated for it! You can also correct the power, but that would slow the plane, moving it out of the perfect speed again... Or wouldn't it?

The real trick is that a plane is mostly efficient at some specific angle of attack, not the airspeed. Airspeed is tied to aoa in such a way, that at a given weight, a given plane will always maintain the same airspeed at the same aoa, regardless whether it's climbing, cruising or descending. For example, 3^O aoa always corresponds with 120 KIAS, for a certain plane; another one may achieve this 120 KIAS at 4,5^O aoa. It depends on airfoils and overall aerodynamic qualities, but it's the aoa that really matters. In general, the faster the airspeed, the lower the aoa.

Let's reiterate the example above.

Plane burns fuel and becomes lighter, as time passes, and it will start to climb, if you left it at previous cruise settings. You can prevent this change in altitude simply by lowering the nose - but that would decrease aoa, which would accelerate the plane (low aoa = high airspeed) and fly faster, than optimum airspeed we have calculated for it! You can also correct the "power settings" and that would slow the plane, while maintaining the perfect aoa we've set for it

You don't need that much thrust (and power) to propel light plane anyway - Cessna really doesn't need that Jumbo turbofan. By the way, now it becomes clear, why most Russian planes had aoa indicator on the panel, for example An-24 is mostly efficient at 3^O. Pretty smart, eh? On Western planes aoa can be read to some degree from attitude indicator in level flight, but that's much less accurate method, than properly calibrated and highly sensitive aoa gauge.

Here are actual test flight data. As you can clearly see, max range and best cruise speeds are the same for a given weight, regardless of altitude and that light plane must fly slower to maintain mostly efficient aoa.

                Vrng Vopt

max gross 20000ft 130 158

        10000ft 131 161

        1000ft 130 164

light         20000ft 114 138

        10000ft 114 142

          1000ft 112 142

This data also hints, how we can use it to our advantage during the flight. Let's just say, that the difference in fuel between "max gross" and "light" was 1000lb. Which means, that for every ~60lb of fuel burned, you have to slow down for 1 knot.

130 - 113 = 17 knots difference.

1000lb fuel difference / 17 = 58,8lb per 1 kt

If your fuel gauges are inaccurate or very small and without any scale, then use fuel flow meter and a clock. 60lb is 10USgal. So after every hour of flight with fuel flow of 10gal/h decrease airspeed by 1 knot. If the fuel flow is 20gal/h (or 2 engines at 10gal/h), then subtract that 1 knot after 30 minutes of flight. And so on.

That's why GA and propeller planes are so fantastic and interesting! You always have something to do and never got bored. Only helicopters can be even more... ekhm, entertaining

"So, you want to be a test pilot?"

+1 to karma for the first one who writes the title of the sim, in which this question was asked

Now you really have all the airspeeds, but before you can do that fuel planning and stuff, you need to perform a test flight. Take your favourite plane or the one that you fly the most or the most extremely. The workhorse of your fleet. The one you enjoy the most. Turn on the following data strips: L/D, total fuel weight and times in your plane doesn't have a clock on panel. Load the plane with full fuel, park it on a ramp and set the day to standard atmosphere (15^OC and 1013hPa), zero wind and zero weather.

1) Note gross weight.

2) Fire up the engine, warm it up, set avionics (set one VOR-DME or GPS to the airfiels you're at, to have range readout during climb) and taxi to the active. Note the fuel before takeoff.

3) Climb with Vy at max power. Every 1000ft note the fuel, time and distance covered.

4) Stop climbing at max reasonable altitude (VSI less than 100fpm or max certified), note the fuel and time for the last time.

5) Now take the plane to altitude midway between max alt and sea level.

6) Set power for best cruise speed and note fuel flow and TAS*.

7) Repeat the above for best range speed and best endurance speed + 10 KIAS.

8) Once again take the plane to the previously specified max altitude. Note fuel and time.

9) Descend to the sea level, while noting fuel weight and time every 1000ft.

* for now, set according to POH or your best knowledge, if POH is unavailable. Engine management and various "power settings" will be covered in one of the next tutorials, time and inspiration permitting.

Now you have full data for educated fuel and flight planning. Basically, you've written yourself a mini-POH essentials You know how much fuel is required for a startup and climb to each and every flight level. You know how much fuel is bured during flight with various important airspeeds and you know how much fuel will be required for a descend. As a required reserve, add fuel amount that would be needed for 45 minutes holding at best endurance speed + 10 KIAS. Additionally, if you're familiar with my "Ded reckon made easy" tutorial, you can calculate time and distance covered during each of the main flight stages (climb, cruise, descens). Just rememeber about IAS-TAS relationship

Armed with that knowledge, you know how fast you should fly. But what about "how high"? As a rule of thumb, I do not climb for more that 1/4 of the whole flight distance. For a 120NM flight, I'd climb for 30NM only. If you've noted fuel, time and distance during test flight climb, then you will know how high you can get during 30NM climb and how much time it would take.

It took me a month to set it up in my head, so it could be written in an acceptable manner and it took more than 7 hours to actually write it down, but in reality it's much more easier to understand and to do

Also I'd like to thank Goran Matovina and Jim Gregory for allowing me to use their creations as guinea pigs during my crazy enterprises. They've made very good and accurate planes and I must say that I've greatly enjoyed flying them as well as digging into all of the performance niuances. Thanks again guys

[Oliver]

Wow Lis... Thanks ever so much! I enjoy reading everyone of your extremely detailed and well written tutorials! Thanks for taking the time to write these wonderful guides!

Oliver

Edit: I beleive the Sim was FSX

[Simmo W]

Thank YOU Lis for yet another excellent tutorial. Are you into training? You should be

[Lukasz]

No, it wasn't FSX. Much older

Unfortunately I'm not in training... yet

Step climbs

I'd like to add one thing to the tutorial, that I have forgot to write. You may have heard of "step climbs" during cruise, which is most often found on airliners on long range flights, but it's applicable to other planes as well. The only requirement to use it is that the flight must be really long, so the difference in weight (and thus optimum airspeed) caused by fuel burn is significant.

As you now know, the lighter the plane, the slower it has to fly in order to maintain proper aoa and thus efficiency. The problem with that is, that people like to get to places fast. If they had the time for an elongated trip, they would have probably chosen a ship or a caravan, instead of plane You can offset it by gradually increasing the altitude, in order to gain advantage from IAS-TAS offset. As the fuel is burned, the optimum IAS will be increasingly lower, but the TAS offset will increase with altitude gained. This offset will compensate for loss of IAS and sometimes it will increase your true speed!

Let's have another look at flight test data (all speeds are IAS!):

                                Vrng  Vopt

max gross    20000ft  130    158

                  10000ft  131    161

                    1000ft  130    164

       

light            20000ft  114    138

                  10000ft  114    142

                    1000ft  112    142

Now, the same chart but with corresponding speeds converted to TAS:

                                Vrng  Vopt

max gross    20000ft  182    221

                  10000ft  157    193

                    1000ft  130    164

       

light            20000ft  160    193

                  10000ft  137    170

                    1000ft  112    142

Let's assume, that the first "step" during the flight has ended on 10000ft. The plane was very heavy with full tanks, VSI has dropped to unacceptably small value and there was no reason to push further up. Lot's of fuel burned for a minimal altitude gain. Plane has accelerated in level flight and achieved either 157 KTAS for max range speed or 193 KTAS for best cruise speed.

As time passed, the fuel was burnt, plane was getting lighter and more willing to climb higher. At the same time IAS (and thus TAS) have dropped by a visibe amount of knots. Now, instead of flying so slow, you push the throttle forward and climb to a higher altitude, let's just say that it would be 20000ft. IAS didn't change much, but look at TAS! This so much slower best range IAS yielded in a TAS that is actually 3 knots faster, than it was at previous altitude and weight. IAS for best cruise speed yieded exactly the same TAS value of 193 knots! It's really amazing, that you can fly slower and faster at the same time, isn't it? In reality you would perform a series of smaller steps, for example 3000ft at a time, but I've left that in such manner to better illustrate the concept.

Flying high has other advantages. Engines are generally more fuel efficient and plane has less drag in thinner air. The air is generally less turbulent and you can overfly the most of bad weather. There are also disadvantages. You really don't want to fly in an unpressurised planes higher than 12000ft without an oxygen mask, because of hypoxia hazard (cannulas are little less efficient in supplying oxygen, but they do have their uses). Also there is cold up there, so better have something warm at hand. There is a very good reason behind these stylish leather jackets that pilots tend to wear, I've purchased such and it makes a fantastic winter clothing

[eaglewing7]

Excellent reading material here, and very true.

A perfect example of which is the Falcon 7X.  The 7X has a maximum certified ceiling of 51,000 feet.  I often use this aircraft within X-Economy, and it is very picky about weights and cruising altitudes.  There is an excellent spread sheet that was put in the .org download manager about cruising altitudes and weights that gives you a very accurate weight to altitude chart. 

This is a plane that loves to fly fast, and high, but do not try and push it to high when it is heavy...

[Pete_SMS]

"So, you want to be a test pilot?"

Could it be that the Sim was

"Chuck Yeager's Advanced Flight Trainer"?

One of my favorite Flight Sims, back in the days on the C64  ;D

[Lukasz]

+1 as promised, in recognition of expertise in flight simulator history I had it on Amiga 500 back in the old days, but that's not the oldest sim I was flying. Sure, by today's standards they were "casual games", but back then, they were mind blowing! I only wonder, what the future will bring?