# Nine Numbers You Need To Know

## As much as we might not want to admit it, aviation is a numbers game. Some of them, like weight and fuel remaining, are more important than others.

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Aviation is a numbers-oriented activity. Sure; we can more or less safely operate an aircraft by disregarding some of them, but if we intend to aviate with some degree of reliability and repeatability—not to mention professionalism—we need to do it precisely, which means using some metric against which to measure our performance and the airplane’s. In the physical world we inhabit, that most often means using numbers.

The good news is we have many different ways of measuring aviation’s various parameters. Altitude, for example, or airspeed. Angle of attack. Not only does the aircraft’s performance depend on numbers, so does our degree of risk. How else can we gauge our progress toward our destination, how much fuel is required and whether we’ll have the weather to land when we get there without numbers?

Keeping track of all the numbers available to pilots can be overwhelming—that’s one reason multi-person flight crews were invented—but our potential for numeric overload can be minimized by focusing on just a few critical ones. What follows are the nine numbers I think are most important for us to know on every flight.

## Speeds

A majority of the numbers we need to know involve airspeed. Thankfully, we have an indicator for that, which incorporates important numbers like never-exceed speed, when we can fully extend wing flaps and when we should expect the airplane to stall. Other important speeds/numbers likely reside in a placard on the instrument panel or sidewall to remind us, but not all of them.

The first number we need is liftoff speed, sometimes called rotation speed. (Large airplanes have a rotation speed, VR, but there’s often not one defined for small ones, so we call it liftoff speed.) This is the minimum speed at which we begin to exert back pressure on the pitch control to take off. This number often is published by the manufacturer as a weight- and conditions-dependent airspeed range rather than a single value. Regardless, it’s one we need to know to simply get off the ground.

Once we’re airborne, of course, we probably want to climb, for which we need a second number, also dictated by conditions. If we’re flying from a shorter field with obstacles, we likely want the airplane’s best angle of climb, VX, offering the greatest altitude gain over distance. Other times, we want to use the best rate of climb value, VY, giving us the greatest altitude gain over time. Frequently, we may want to use both numbers as we climb, but for our purposes, we’ll consider them the same.

As with other airspeeds we need to know, optimum climb speeds will vary with both weight and altitude. The sidebar “How Climb Speeds Change With Altitude” below goes into greater detail.

Our third number likely is present on an instrument-panel placard as a maximum value—maneuvering speed, VA. The trick is VA actually is weight-dependent, and the placarded value often is for maximum gross weight. At the end of a long trip with few people and little baggage, for example, this number should be reduced from what the placard says. The sidebar, “Adjusting Maneuvering Speed For Weight,” below has a useful rule of thumb.

The fourth number we need to know on each flight is specific to single-engine airplanes: the best engine-out glide speed. For many types, this will be a single value published by the manufacturer for a gross-weight airplane. Others may come with a narrow range of weight-dependent values to use when the engine quits. The FAA’s Safety Briefing topic, “Best Glide Speed and Distance,” explores how best glide changes with weight. See the sidebar “Best Glide Speed” for more.

## Weight

As the foregoing discussion details, many airspeeds we use on a daily basis are weight-dependent, and our airplane’s documentation may include only one value, valid at maximum gross weight. Of course, we’re never at max gross after taking off. The difference may be minimal and of no consequence on initial climb, but three or four hours later it can have greater impact. So it’s important to know the airplane’s weight, our fifth number.

Typically, when we discuss weight, we also talk about balance—where the center of all that weight is located on the airplane’s longitudinal axis. We call that the center of gravity, of course, or CG. That’s an important pre-flight number to know, but has less utility as the flight progresses when considering our nine numbers. That said, it’s important to know two things about the weight’s location: where it is at takeoff relative to the allowable range, and where it will move as fuel is burned. The center of gravity of some airplanes (cough, Bonanzas, cough) will move aft as fuel is burned; with other airplanes, it may not move appreciably at all, or will move forward.

Any CG shift with fuel burn has implications for stalling speeds but primarily affects pitch stability. Aboard an aforementioned Bonanza, the rearward shift as fuel burns moves the CG closer to the center of lift, one effect of which is to reduce pitch stability, and an input we make to the pitch control near the end of the flight will have greater effect than when we took off. If you regularly fly an airplane whose CG shifts appreciably as fuel is burned, it’s less important to know the specific CG value than it is to know the airplane’s handling will change when you punch off the autopilot after five hours of cruise flight. That said, your pre-flight planning should include a weight and balance calculation that considers the airplane’s state at the destination, when you’ve burned off all that fuel. It’s not unheard of for it to be outside the allowed envelope.

Of course, we know—or at least should know—the airplane’s weight at takeoff. Unless we’re throwing Momma from the plane, flying jumpers for a drop zone or dropping fire retardant, the only way for the airplane’s weight to change during flight is by burning fuel. If we’re burning 10 gallons an hour, for example, the airplane becomes lighter by one pound every minute and after a four-hour flight, the airplane weighs 240 pounds less. The impact of this weight change, absent any CG shift, can materially change the other numbers we need to know.

Considering the magnitude of the weight change is relatively easy. If we’re burning 10 gph and the airplane weighed 2400 pounds at takeoff, it now weighs 10 percent less. The speeds you use for optimum performance should be adjusted accordingly.

## Environment

Weights and appropriate speeds are some of the basic numbers we should know at all times, but so is the ambient temperature and wind velocity, the sixth and seventh of our nine numbers. Why? Because even if slight variations in them may have no real impact, they have a material impact on performance (temperature) and planning (wind).

Every takeoff, landing or cruise performance chart we’re aware of considers temperature as a variable to be plugged into the calculations. For example, it’s not unheard of for the same airplane at the same weight to require half as much runway in the winter as it does in the summer. And if you’ve done any serious mountain flying, you know it’s always better to take off in the morning when it’s cooler than at midday.

Wind velocity—its speed and direction—also figures prominently in performance, as anyone who’s inadvertently taken off or landed downwind can attest. Even when we don’t make such a mistake, crosswind landings and takeoffs can be unforgiving in exacting their toll in bent sheet metal, ruined runway lights and flat-spotted tires. Both taken together also impact our cruise performance.

Of the two, temperature generally is more important when considering takeoff and landing performance while the wind at altitude can mean the difference between a non-stop flight or landing to take on more fuel. A cross-country flight I made years ago highlights this: The winds at altitude offered something like a 20-knot headwind while those at lower altitudes were light and variable. I flew the trip at 2500 feet msl, shaving an hour off the en route time needed at 11,000 feet.

## Time And Fuel

Which brings us to our eighth and ninth numbers, time and fuel, which should be no-brainers: How long will it take to get to our destination? Do we have enough fuel to get there? The advent of GPS navigators and electronic flight bags makes the time question stone-age simple to answer, but that’s only half the game. We also need to know if we have enough fuel to get there. Relatedly, it’s nice to know we’ll arrive before the destination airport socks in, forcing us to divert, or the FBO closes. The accident summaries at the back of this magazine, meanwhile, rarely go a month without including an example of someone who ran out of fuel.

In fact, it may be easier for us to consider available fuel as time in the tanks. The need to know how much time we have available to remain aloft and how long it will take to get to our destination should be obvious, but it’s amazing how often someone forgets these basic numbers.

## Stringing It All Together

The proper speed to fly, the airplane’s weight, the wind and temperature, and the time and fuel remaining are essential numbers we need to know during each flight. In fact, many of them are interrelated—the airplane’s weight can help determine what speed to fly and when, even if the extremes often are separated only by a knot or three. The time remaining in our tanks directly impacts where we can go and when we’ll arrive while also affecting weight.

Given the devil-may-care allure of kicking the tires and lighting the fires that afflicts many pilots at some point, we may not want to admit—to ourselves or anyone else—that there are limits on what we can do with an airplane or what the airplane can do for us. But flying is a numbers game, and we need to understand and respect how the value of certain parameters directly impacts performance and safety. And thanks to the aforementioned GPS navigator and electronic flight bag, which are capable of planning things down to the tenth of a gallon or pound, there’s no excuse for not being able to answer at any time questions like how fast I should be or how much this thing weighs.

## Adjusting Maneuvering Speed For Weight

We were trained that maneuvering speed (VA) is the speed above which full or abrupt control movements must not be made. Later, we learned we also shouldn’t fly in turbulence above this value. But we’re often not trained to reduce VA at lighter weights, although we should.

Recent AFMs/POHs and those for newer airplanes often include more than one maneuvering speed, for heavy, medium and light weights, perhaps labeling them “operating maneuvering speed,” or VO, as shown in the excerpt above, adapted from the Diamond Aircraft DA 62’s AFM. For those of us flying airplanes without such detail in their documentation, computing your weight-adjusted VA/VO is easy enough to do in your head using a rule of thumb. You simply need to know two values: the airplane’s maximum gross weight and its current weight.

The rule of thumb is for every two percent reduction in weight from max gross, reduce VA by one percent. As an example, presume an airplane with a 3600-lb maximum gross weight and a 110-knot maneuvering speed is being flown at 3000 lbs. That’s roughly 83 percent of its gross weight, for a 17-percent reduction from maximum. Half of 17 is 8.5. Reduce the 110-knot value by 8.5 percent, which gives us a rounded, new weight-adjusted maneuvering speed of 101 knots.

If doing math in your head isn’t your thing, you can make up a table with various weights and the appropriate speed, then tape it to the instrument panel, or include it in your electronic flight bag’s documents. In any event, remember that VA/VO is the maximum speed we should be flying in turbulence; this is one of those occasions when slower is better.

## Best Glide Speed

When your single’s engine quits, you’re flying a glider. Among other tasks, you need to fly the airplane. But at what speed? Manufacturers give you a target number to use—the airplane’s best glide speed. The bad news is that a single number doesn’t tell the full tale because it’s usually published for maximum gross weight and should be revised downward at lighter weights.

The table at right presents the published weight-adjusted values for three popular singles. Notably, it’s a relatively recent trend for AFM/POH data to include such a range. For example, the POH for a 1977 Cessna 182Q Skylane contains a single number: 70 KIAS, at the airplane’s 2950-lb. gross weight.

The FAA’s Safety Briefing topic, “Best Glide Speed and Distance,” says the number will be “roughly halfway between VX (best angle of climb speed) and VY (best rate of climb speed).” The publication highlights the difference between best glide speed—which offers the greatest distance over time, versus minimum sink speed, the speed resulting in the lowest descent rate. The publication recommends doing some in-flight testing to nail these speeds for the airplane you fly.

## How Climb Speeds Change With Altitude

Putting aside the effects of weight on important airspeeds, we also need to understand how altitude impacts climb performance. Simply stated, best angle of climb (VX) increases slightly with altitude while best rate of climb (VY) decreases at a slightly higher rate. The graph at right shows the relationship, and that the two values are the same at the airplane’s absolute ceiling.

As we climb, there’s less air available to generate lift or make power. Since an airplane can climb only when available power exceeds what’s necessary to maintain altitude, the maximum climb angle occurs when the difference between power available and power required is the greatest. As power is reduced by altitude, maintaining VX places the airplane behind the power curve. To maintain the maximum angle of climb, we must lower the nose and accelerate. Meanwhile, when climbing at VY, best rate of climb, the less-dense air means less lift is being generated. To compensate and achieve maximum climb rates, we need to increase the angle of attack, which means flying more slowly.

This admittedly is something of a simplistic explanation; there’s more going on here—including propeller efficiency, induced and parasite drag and the relationship of true airspeed to indicated— than space allows. We’ll revisit this topic in an upcoming issue.

Jeb Burnside is the editor-in-chief of Aviation Safety magazine. He’s an airline transport pilot who owns a Beechcraft Debonair, plus the expensive half of an Aeronca 7CCM Champ.

This article originally appeared in the January 2021 issue of Aviation Safety magazine.

### Picture of the Week, June 24, 2021

1. Yes, but …

Yes, we know this if we have ever looked seriously at a POH but almost no one says why. The answer to that question is pretty simple: it all stems from the coefficient of lift, where lift varies by angle of attack (AoA) and by the square of the dynamic pressure, which means it varies by the square of calibrated airspeed.

Think about this for a moment: when we put more stuff in the airplane it gets heavier and therefore the wing has to produce more lift to carry it around. We can AoA by pulling on the stick or yoke, but only up to a point (critical AoA). We can also push the wing through the air faster to generate more lift at the same AoA.

I teach my students how to calculate these changes and then require them to work out new numbers from from the published numbers in the POH. As you mentioned in the article almost all the V-speeds are relative to max gross weight. When was the last time any of us landed our airplanes at max gross weight? That means that published speeds are going to be too fast. The only place in most POHs where there this is addressed is for determination of Va and then only cursorily. The calculation for correction of these factors is actually pretty simple. Here it is:

V’ = V * sqrt( GW/MGW)

In words that means that the new v-speed (V’) is equal to the max gross weight v-speed (V) times the square-root of current gross weight (GW) divided by max gross weight (MGW).

For example, let’s take Vs0, stall speed in landing configuration. The POH for our example aircraft says that stall speed is 60kts, the bottom of the white arc on the airspeed indicator. Max gross weight for our airplane is 3000 lb but I am at the end of a long cross country by myself and I am down to about 1/4 fuel. I am nowhere near MGW. Let’s imagine I am really at 2400lb. Let’s see what that does to my stall speed:

53.6 kts = 60 kts x sqrt( 2400/3000 )

That also means that my approach speed (1.3 Vs0) should be 70 kts instead of 78 kts. Is it any wonder that we watch airplanes float forever and overshoot their landing spots by many hundreds of feet?

Now this doesn’t change all our V-speeds exactly the same way. The relationship of Vx and Vy is a bit more complicated but this will get you into the ballpark. For other V-speed like Vs, Vr, Vref, Vg, and Va, this calculation is spot on.

Some POHs get this right. Starting around 1980 Mooney began publishing a chart of Vref speeds vs. weight right on the landing performance chart. I find it amusing to ask clients why they think that chart is there and watch the deer-in-the-headlights look. After a few moments I give them the answer, “Because that is the speed Mooney wants you to fly.”

So even if you don’t have the benefit of the manufacturer doing the work for you, there is no reason not to do this for yourself and post it somewhere in your airplane where you can reference it.

2. Excellent topic.

A few numbers should be engraved on inside of eyelids. 😉

Clarification:
Rotation speed is not liftoff speed, there is a delay after rotation before liftoff occurs. Depends on airplane of course, for big iron a definite rotation angle is needed (original B737 will be light on wheels by rotation time).

Biggies use V2 as initial climb target if an engine resigns after decision speed, IIRC for original 737 use V2+15 for

A fine point is to understand your units of speed, knots being 15% larger than mph.

Stall speed is an essential number, varies not only with weight but bank angle – in BC many crashes occur when pilot gets into a box canyon and goes to slow trying to turn back with trees looming into windshield. Likely better to mush into trees than fall onto rocks from stalling. Extend flaps I suppose, to reduce stall speed. Have a plan, besides one to avoid getting into a box. (The COPA convention in Red Deer AB taught mountain flying, one tactic was to cross a ridge at an angle to give you more time to figure out if you were heading into the correct pass through the huge rocks called Rockies. Many flatlanders attended, they being anyone from east of Red Deer. 😉

In a bank the wing has to generate more lift to force the machinery into a turn, you bank to create ‘centrifugal force’ as you don’t have a rope holding you to the centre of the circle, hence stall speed increases.

3. Completing:
Biggies use V2 as initial climb target if an engine resigns after decision speed, IIRC for original 737 use V2+15 for initial climb with all engines producing thrust. Changing speed with flap retraction.

Boeing did a big study on what made 737 operations successful, ‘Fly the numbers’ was a key element for success.

4. Besides eyelids, QR cards are a VGI.

Pacific Western Airlines used a round card that fit in the old radar display, on which V1, Vr, and V2 were written to suit the particular takeoff weight and flap setting used.

(V1 being takeoff decision speed for multi-engine airplanes.
For landing, Vref is calculated as giving a margin above stall for approach, adjusted on the fly for wind and gusts.)