V speeds

(kias: knots indicated airspeed; kcas: knots calibrated airspeed; ktas knots true airspeed)

V speeds [Wikipedia] are the critical performance speeds of an aircraft — while some of them are illustrated on the face of the airspeed indicator using lines and bands of different colours, a pilot is usually expected to be able to cite them from memory for each aircraft she flies, off by heart, backwards, while standing on her head drinking a glass of water. For example, my Warrior stalls
at 44 kias dirty (Vso) and 50 kias clean (Vs), best angle of climb (Vx) is 63 kias, best rate of climb (Vy) is 79 kias, and so on. Simply memorizing isn’t always enough, however, because of a couple of gotchas.

Gotcha #1: indicated vs. calibrated airspeed

The first gotcha isn’t usually too serious, but it’s worth keeping in mind when comparing different aircraft, and it becomes critically important for gotcha #2. All of the V speeds are given as indicated airspeed, so that the pilot can read them straight off the airspeed indicator. With the flaps up in the middle speed range, usually around Vy, indicated and calibrated airspeed are about the same; however, under other circumstances, it gives a distorted picture of how fast you’re actually going:

  • at lower speeds, indicated airspeed is almost always slower than the real, calibrated airspeed; for example, the Cessna 172p has a Vs (stall, clean) of 44 kias, but that’s actually more like 51 or 52 kcas — the plane’s not actually landing as slowly as you think it is, though the performance tables in the POH take that into account
  • at higher speeds, indicated airspeed is almost always faster than the real, calibrated airspeed; for example, the Cessna 172p cruises at about 111 kias at 75% power (120 ktas at 8,000 ft), but that’s actually more like 108 kcas
  • flaps distort the airspeed indication even more — dropping 10° flaps in the 172p at slow speeds makes the indicated airspeed read 9 knots slower than the calibrated airspeed

It’s easy to notice that these errors tend to work in the aircraft manufacturer’s favour — who doesn’t want a plane that lands slower but cruises faster? There may be other engineering reasons not to mess with the airspeed indicator, but it does not look like it would be difficult to design an ASI that shows something closer to the actual calibrated airspeed, at least with the flaps up.

Gotcha #2: weight, balance, and wing loading

Most of the V speeds apply only when the aircraft is being flown straight and level in coordinated flight at maximum gross weight with the centre of gravity (CG) somewhere in the middle of its allowed range. Shifting the CG has only a tiny effect on V speeds (typically a knot or two), but the other factors can play big.

Roughly speaking, most V speeds will vary proportionally to the square root of the aircraft’s weight. For example, if an aircraft stalls at 50 kcas at 2440 lb, it will stall somewhere around 46 kcas at 2000 lb. Here’s the formula, for anyone who’s interested:

sqrt(weight / maximum weight) * V speed

2000 divided by 2400 is 0.82, the square root of that is 0.91, and 0.91 * 50 is 45.5. Note however, that you have to do the math on the calibrated airspeed, not the indicated airspeed, to get this right, especially since the variation between the two gets huge near the stall speed.

This math works in your favour when you’re flying light, but it works against you in a turn. In a coordinated, non-descending 60° bank, the aircraft is double its normal weight, so a 2440 lb aircraft actually weighs 4880 lb. Running the same formula, the stall speed will be multiplied by sqrt(2), or approximately 1.4. If the aircraft normally stalls at 50 kcas, it will stall at about 71 kcas in that turn. Smaller bank angles still have a significant effect on stall speed, and can be especially dangerous while maneuvering right after takeoff or just before landing, when the aircraft is already slow.

Maneuvering speed

One place that the POHs do take this into account is the maneuvering speed (Va), the maximum speed for abrupt maneuvers, such as recovering from upsets in moderate or severe turbulence. Typically for light, non-aerobatic aircraft, Va is roughly double the stall speed (calculated using calibrated speeds), so that the wing will stall under a load of more than 4Gs (double the speed will lift four times as much weight, more or less). This is critically important not only for protecting lifting surfaces like the wings and horizontal and vertical stabilators from excessive loads, but also for keeping the engine from ripping off its mount though sudden accelerations. As a result, POHs generally give VA not as a single number, but as a range — for my Warrior, it ranges from 88 kias (89 kcas) at 1531 lb to 111 kias (108 kcas) at 2440 lb. Running the above formula on the 108 kcas at 2440 lb gives a result of 86 kcas at 1531 lb, which is 3 knots low, but pretty close.

Cutting speeds to increase safety margins

As mentioned earlier, nearly all of the V speeds actually work this way. Most of the time, pilots don’t have to worry, but if you’re flying in and out of short, obstructed fields, doing the math can be a huge help. For example, if you normally fly an approach with full flaps at 63 kcas at 2,440 lb, and your plane is loaded only to 1,900 lb, you can fly the approach at 56 kcas (don’t forget to convert to kias!) and shorten your landing distance without giving up your safety margin; likewise, if your Vx (best angle climb airspeed) is 60 kcas at 2,440 lb, you can climb out at 53 kcas and clear the trees by a few more feet. If you want to get above the turbulence quickly to keep from getting sick, you can adjust Vy down as well — if you normally climb out at 79 kcas, climbing at 70 kcas will get up higher, faster, at this light weight (though it might not let your engine get enough airflow for cooling).

Of course, if you have a long runway, no trees in the way, etc., you probably don’t need to worry about these calculations, since the published V speeds give you an extra safety margin. Just make sure that you don’t add an extra extra margin when you’re flying light — if your normal approach speed is 70 kias, the plane is lightly loaded, and the air is a bit rough, you already have about a 9 kt safety margin, so there’s no need to add another 10 kt and approach at 80 kias, increasing your landing distance even further. One reason that people claim that more powerful aircraft “float a lot” on landing is that those aircraft often have much higher maximum gross weights, so when a pilot is flying one of them alone (and thus, very light), he usually approaches way too fast.

Airliners and other larger aircraft make calculations like these for every flight. There is no fixed V speed to do a takeoff or landing in a 747, for example; instead, the dispatcher or a computer on board calculates the optimal speeds based on fuel, cargo, and passenger load for each trip. After all, for a 747, an 8,000 ft runway is a short-field landing.

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5 Responses to V speeds

  1. John says:

    The FAA’s Airplane Flying Handbook has a small section on this topic, but I think your version is more readable. I find student pilots often overlook the formula for adjusting V-speeds for less than gross weight.

    Another way to approximate Va is to multiply Vs by the square root of the maximum positive load factor for the aircraft. I like to teach this to students so that they see the relationship between stall speed and maneuvering speed. The maneuvering speed is calculated so that if turbulence causes the wing to reach the critical angle of attack, the wing should stall (and unload) PRIOR to exceeding the maximum positive load factor.

  2. Marc says:

    Great job! I’m a CFI/ATP with 4100 hrs. and I’ve yet to see a better explanation of how to adjust POH V-Speeds for weight.

  3. Dave Starr says:

    I was a bit put off by your first paragraph. I’m only a private pilot and a long-inactive one at that, but all the critical performance and limit speeds I’ve ever seen marked on a cockpit instrument have been on the airspeed indicator, not the altimeter.

    I’m not sure if this was your gotcha or Wikipedia’s, I find that site pretty useless myself in most any technical area, but like bubble-brained TV newscasters and newspapers that don’t know their country’s geography, it seems very popular in today’s world.

    A very good job, though, on explaining a _lot_ about critical speeds I never learned.

  4. david says:

    Thanks, Dave — “altimeter” was just a simple typo (you’ll notice that the picture is an ASI), and I’ve corrected it. I find that Wikipedia is actually pretty good on technical topics once an article settles. The trick is learning to recognize an article’s level of maturity, which isn’t easy at first.

  5. I was searching the effect of center of gravity on aircraft behavior in turbulence, and discovered your blog. I look forward to going through your archives. Good information.

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