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Trivia Testers

To the nearest 100 feet, estimate the takeoff distance into a 13 knot headwind for an airplane with a 52-knot takeoff speed where, based on current conditions of temperature, pressure, runway surface, slope, etc., the no-wind takeoff distance is given as being 1000 feet. Then estimate that distance with a 13-knot tailwind.

Curious Names of Remarkable People
Much has been written about Glenn Hammond Curtiss, and he has been mentioned in several of these Trivia Testers. In September 2002, you might recall reading about the Aerial Experiment Association, founded by Alexander Graham Bell (and which included Glenn Curtiss among its members, along with US Army officer Thomas Selfridge). A curious coincidence is that the chosen site of the AEA was Hammondsport NY, where Glenn Curtiss was located, and (as some may have noticed) the middle name of Glenn Curtiss was Hammond. So, was there any connection?

  1. Glenn Curtiss' great-grandfather, Hammond Curtiss, was an early settler in the area, and the town was named in his honor.
  2. absolutely none: It was only a coincidence.
  3. Hammondsport was his mother's home town, and she chose it for no other particular reason.
  4. Glenn Curtiss was actually given no middle name. Convinced that a middle name would add some level of credibility to his work, he added it in 1906.

Answer: C. I wondered about that for the longest time. I finally got my answer from Seth Shulman, the author of the Curtiss biography "Unlocking the Sky". As he told me, the answer was found by Curtiss' first biographer, Clara Studer. Glenn Curtiss' mother gave him the middle name Hammond after her beloved hometown. (In addition, she decided to name him Glenn after a visit to the dramatic Watkin's Glen, not far from her home.)

Broken Arrows
The United States has (so far) been the only nation to drop an atomic weapon on another country. As everyone knows, we dropped two atomic bombs on Japan during World War II (and it was this which, in fact, hastened the end of that war). Okay then... True or false: The United States has never dropped the more powerful hydrogen bomb on any country--either during times of peace, or while we were at war.

Answer: False. There are also rumored incidents involving nuclear weapons belonging to other countries. Actually, the term "incident" is a tad misleading, and the word "accident" might be more fair. Applied to ourselves, that would hopefully be the case, because we've had our share of nuclear "oopsies", around 30 of them. Although the release of radiation sometimes ocurred (along with the horrendous clean-up logistics), none involved an actual thermonuclear detonation. However...the conventional explosives that are used to start an atomic explosion have caused the widespread release of fissionable material. The two best known such events were that at Palomares in Spain, in January of 1966 and near Thule in Northern Greenland, also in January, 1968...

In 1966, we dropped four thermonuclear bombs on Spain. Yes, Spain. (Each weapon had about a one Megaton yield.) It was Palomares, Spain, to be exact. The term "dropped" here is also a bit misleading; it's more like they "fell". (No, we didn't do it on purpose.) In mid-January, 1966, a SAC KC-135 tanker and a B-52 bomber carrying four hydrogen bombs collided while refueling over the Mediterranean coast. Three of them (as well as pieces of the wreckage) fell near Palomares. The fourth bomb fell into the Mediterranean and was later recovered, intact. Although one bomb landed in a dry creek bed, the other two of those three bombs exploded during their fall (the conventional "TNT" part, I hasten to add, and not the plutonium), and fissile material was scattered over about a one square mile area. About 1,400 tons of contaminated material were removed for storage back in the USA. The over 700 people who were in the vicinity at the time have been evaluated over the subsequent quarter-century, but even the Defense Nuclear Agency said, in 1975, that the total extent of the damage will never be known.

Four seems to be an unlucky number here. Just over two years later, a B-52 with four one-Megaton weapons sustained an in-flight fire and crashed on the ice about 10 miles from Thule Air Base in Greenland. The impact with the ice detonated the weapons' conventional explosives, spreading plutonium-239 over a small area (this time, only several acres in size). Several pounds of plutonium were found on the ice, as well as on many thousand pieces of wreckage. An unknown amount was also carried out to sea with the smoke that rose into the air. About a pound of Pu-239 (broken up into very small pieces) was subsequently found on the seabed. Immediately after this second accident, American aircraft were forbidden to carry such weapons on routine flights.

And lest you think we only did it to other countries, we've also done it to ourselves about equally as much. Before either of these incidents for example, in Februray 1958, a B-47 bomber had a midair with an F-86 fighter southeast of Savannah, Georgia. The pilot was ordered to jettison the bomb in order to land safely. Unfortunately, it was nighttime and no one paid enough attention to exactly where it fell: somewhere along the southern shore of uninhabited Little Tybee Island. It has never been found. A few weeks later incidentally, another H-bomb was accidentally dropped, this time near Florence, South Carolina.

On A Roll
To the nearest 100 feet, estimate the takeoff distance into a 13 knot headwind for an airplane with a 52-knot takeoff speed where, based on current conditions of temperature, pressure, runway surface, slope, etc., the no-wind takeoff distance is given as being 1000 feet. Then estimate that distance with a 13-knot tailwind.

  1. 1000, 1000
  2. 800, 1200
  3. 600, 1600
  4. 400, 1900

Answer: C. The given takeoff speed and takeoff roll were hypothetical numbers, but they are more or less representative of ballpark figures for a Cessna 172. For starters, are the numbers given in choice A realistic? No, and you can relax; choice A is laughably out of the running; I threw that in just to start you thinking. Okay: you probably noticed that 13 is exactly one quarter of 52. First off, a wind that's one quarter of your takeoff speed cuts the takeoff roll almost by half, and in the case of a tailwind, increases it again, by more than half. The exact mathematical formula for determining the effect of a headwind on takeoff distance is given by Dw = Do(1 - W/Vr)2, where "Dw" is the corrected takeoff distance, "Do" is the no-wind takeoff roll, "W" is the wind velocity and "Vr" is the takeoff airspeed. In words, you take the headwind divided by the takeoff speed, subtract that quotient from one, square the result, and multiply that in turn by the distance for a no-wind takeoff roll. The "tailwind effect" formula is similar, differing only by there being a plus sign instead of a minus sign in the parentheses. It becomes Dw = Do(1 + W/Vr)2.

For a 13 knot headwind, you get:
1,000 x (1 - 13/52)2 = 1000 x (1 - 1/4)2 = 1000 x (3/4)2 = 1000 x 9/16 = 9,000/16 = 563 ft.

For a 13-knot tailwind, that's:
1,000 x (1 + 13/52)2 = 1000 x (1 + 1/4)2 = 1000 x (5/4)2 = 1000 x 25/16 = 25,000/16 = 1563 ft.

Of course, you've probably heard of the even-simpler rule of thumb that a 10% headwind (that is, 10% of liftoff speed) reduces the ground roll by 19%, and a 10% tailwind increases the ground roll by 21%. This rule is exactly correct in fact, but only when the wind is exactly 10% of the takeoff speed (and of course, when there is no wind). Using multiple proportions at higher wind speeds (say by doubling that 19% when the headwind is 20% of liftoff speed) introduces errors--small at first, then progressively greater. The problem is that this rule of thumb approximation yields takeoff distances which are increasingly optimistic underestimations of what you would really need. For instance, with a headwind of 20% (in this case, 10.4 knots) you would come up with a takeoff roll only three percent shorter than if you had used the formula (620 feet, versus 640 feet). With a 30% headwind (15.6 knots) your optimistic underestimation represents a 12% error (430 vs. 490 feet). And with a 40% headwind, or 20.8 knots (by which point, in reality, you would probably be questioning your ability to taxi to the runway, let alone take off), this error becomes 33% (240 vs. 360 feet). Similar errors exist for the tailwind side of things, but the error (again, optimistic, or shorter than you would actually need) is much less: about 1% at 10 knots, 4% at 16 knots, and 6% at 20 knots (and very academic, since no one in their right mind would really take off the wrong way, with a wind that strong). Incidentally, for those mathematically inclined who might be wondering, the decrease in takeoff roll goes down by "X" times when headwind is exactly (1 - 1/SQRT(X)) of the takeoff speed, and the increase in runway needed goes up by "X" times when headwind is (SQRT(X) - 1) of the takeoff speed. Also, the formula for decrease and increase in takeoff times (taking off against and with a wind, respectively) are similar to the distance formulas, except there is no "square" exponent.

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