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Whenever you have seen a large airplane land, there is always a screech and a puff of smoke when the tires first contact the runway. You may have noticed another symptom of this when taxiing on the runway while preparing to take off. There are a LOT of tire skid marks right where the large airliners first touch down on the runway. In fact, a regularly scheduled chore of all major airports is to shut down each runway to remove those accumulations, as once the tread accumulations have gotten several inches thick, a new danger to the aircraft remaining under control exists!
If you do much flying, you might try to look at how extensive the skid marks are on any particular runway, as that is an indication of where in that maintenance schedule that runway happens to be. It would probably be really interesting to see a timelapse movie (over several months) of that spot on a runway where airliners first touch down. In addition to all the puffs of smoke and the screeches, the accumulating deposits of tire tread on the runway should be frighteningly obvious!
Recently, I heard in a TV commercial that American Airlines has 3,900 flights every day, which means 3,900 landings every day. They do not seem to want to admit how long tires last, but comments from Airport and Airline Technicians seem to indicate that 100 landings seems believable. That means that, every day, just that single airline needs to replace 39 full sets of airliner tires! They also seem not to want to divulge the total cost of removing a huge wheel from an airliner, dismounting the tire, installing a new tire, balancing it, testing it and remounting the wheel on the airliner, including highly paid technicians, but $5,000 per tire seems likely reasonable. That suggests that American Airlines must spend around two million dollars every day on replacing tires! Imagine if the tires lasted a hundred times or four hundred times as long! That one company would save nearly two million dollars every day!
On your car, you buy a set of tires that last for 40,000 miles or more. Airplanes spend much of their lives in the air (or parked). Their tires are only moving on the ground during the onemile runway run and another mile to the terminal. Their VERY advanced, very expensive tires have a tread life on the scale of one hundred miles!
OK! When could enormous wear occur? During low speed taxiing? No, there is extremely little tire wear under those conditions. During a takeoff? A moderate amount of wear can occur then, due to the fairly high speed attained just before liftoff. But that cannot possibly account for a tire tread lifetime of just a hundred miles or so.
There are two situations during landing that can (and do) wear the tires extremely rapidly. Prior to large airplanes having ABS brake systems, it was possible for a pilot to apply the brakes so aggressively in slowing the plane down that he could "lock up" one or more of the wheels. If that wheel remained in that position, a LOT of wear could occur on one side of that tire, resulting in something called "flatspotting". That is virtually unheard of today because of the automatic action of ABS brakes.
That leaves only one remaining situation that can result in rapid wear in the tires, at that instant of touchdown, when the very heavy nonspinning wheel and tire assemblies must suddenly be sped up to 130 mph (110 knots) by friction with the pavement of the runway. This fraction of a second, mentioned above, with its puff of smoke from wearing of tire tread and its skid marks that are additional parts of the tire that came off, is therefore the cause of virtually all of the wear on aircraft tires. In Physics terms, the contact with the runway must apply an enormous moment (torque) to give the tire/wheel an angular acceleration to get the rotation up to the necessary speed to avoid further skidding.
In Engineering terms, it is fairly simple to estimate the necessary Torque necessary to accomplish such a spinup, given just the time interval involved and the rotational inertia of the tire and wheel assembly. The time interval and the necessary final rotational speed ω determine α the rotational acceleration. (ω = α * time) The necessary torque is defined as equal to the product of α and (I) the rotational inertia. (torque = α * I) And the necessary frictional force between the tire tread and the runway is (Force = torque / radius) By knowing the radius of the tread, and these other well known values, it is then easy to determine the necessary frictional force at the tire/pavement interface. These are all very simple and traditional Engineering calculations.
For a general aviation (light aircraft), which weighs 2200 pounds at landing, which lands at 70 mph and which has 6.00x16 tires and wheels:
2200 pounds weight is equal to 69 slugs of mass (don't ask!). 70 mph is equal to about 103 ft/second. Therefore, the kinetic energy of the airplane just before touchdown is 1/2 * m * v^{2} or 0.5 * 69 * 103^{2} or about 364,000 ftlb of energy.
In order to stop, all that kinetic energy has to be removed. Newton told us that energy cannot be created or destroyed, so it all must be converted into some other sorts of energy. Let's see how much is involved to spin up one wheel/tire.
That size tire is around 26" in diameter, and the tire and rim weighs around 25 pounds. There is a quantity called the Rotational Inertia for spinning things that is sort of like the Mass for s something going straight. The Rotational Inertia is usually called I, and it is calculated by m * r^{2}. M is the total mass of the wheel/tire, or 25/32 slugs. R is an effective radius, which is sort of hard to explain simply. In this case, it is around 8" or 2/3 foot. So I is equal to 25/32 * (2/3)^{2} or 0.35 slugft^{2}.
We also need to know how fast the tire will be spinning when it is fully at speed. We commonly describe this as in RPM, but in Physics, it is more useful to describe it in radians/second. In this example, once the tire stops skidding, it will be spinning at the aircraft speed/tire circumference times per second (or 103/6.8) revolutions per second and we just multiply that by 2 * PI to get radians/second, or 95 rad/sec.
The kinetic energy of rotation that the wheel/tire will eventually have is given by 1/2 * I * ω^{2}. In our example, it is 0.5 * 0.35 * 95^{2} or 1580 ftlb. The aircraft has two main tires/wheels, so double this to 3,160 ftlb.
So, if the aircraft has 364,000 ftlb of kinetic energy the moment before touchdown, it will have around 361,000 ftlb left after fully spinning the wheels/tires up! An almost irrelevant effect as regarding stopping the aircraft. This is mentioned here because a number of critics have informed me that it is "long known" that the landing distance would be 20% longer if the tires were prespun. Apparently, no one has ever done the math, because that is clearly not the case! In the case of this aircraft, if it normally took 500 feet before stopping, if the wheels were prespun, it would take 503.3 feet, slightly more than one yard longer! NOT 20% longer. Not even 1% longer!
Yes, the aircraft had that 364,000 ftlb of kinetic energy to dissipate in order to stop. But upspinning the tires absorbs an extremely small amount of it. Actually, if the aircraft began the landing at 69.75 mph instead of 70 mph, there would be a much greater effect of shortening the landing!
400,000 pounds weight is equal to 12,500 slugs of mass. 130 mph is equal to about 191 ft/second. Therefore, the kinetic energy of the airplane just before touchdown is 1/2 * m * v^{2} or 0.5 * 12500 * 191^{2} or about 227 million ftlb of energy.
That size tire is around 8 feet in diameter, and the tire and rim probably weighs around 1000 pounds. The Rotational Inertia is equal to 1000/32 * 2.5^{2} or 195 slugft^{2}.
Once the tire stops skidding, it will be spinning at 191/25 revolutions per second and so ω is 48 rad/sec. (The giant wheels actually spin more slowly than the small aircraft tires do!)
The kinetic energy of rotation that the wheel/tire will eventually have is then 0.5 * 195 * 48^{2} or 225,000 ftlb. The aircraft has sixteen main tires/wheels, so this total is 3.6 million ftlb if kinetic energy needed to upspin all the main landing gear tires/wheels..
So, if the aircraft has 227 million ftlb of kinetic energy the moment before touchdown, it will have around 223 million ftlb left after fully spinning the wheels/tires up! Again, an almost irrelevant effect as regarding stopping the aircraft.
Say the 747 normally takes 5,000 feet of runway to completely stop. We can easily calculate the deceleration that occurs. Another Physics formula is 2*a*d = v^{2}. We know everything but a, 2 * a * 5000 = 189.06^{2}. Solve for a and get 3.5744 ft/second, a gentle deceleration of around 1/10 G.
Let's see how far that exact same aircraft would have taken to stop
if it had prespun the wheels/tires, and applying the same deceleration!
Same equation:
2 * 3.5744 * d = 191^{2}. This gives 5103 feet as the needed
landing distance, roughly one hundred feet longer, half the length of
the aircraft. That also is certainly not any "20% longer landing
distance"!
In a very small fraction of a second, the heavy wheel and tire assemblies must be spun up to the 130 mph (191 feet per second) tread speed. From the lengths of runway skid marks (seemingly under 20 feet), this seems to occur in well under 1/10 second. Simple calculations show the extreme frictional forces present at the tirerunway surface. This is certainly the cause of extremely rapid tread wear on the tires, which is apparently virtually the only wear that occurs during their lives. (Additional math is not presented here because you have been punished enough!)
I have a feeling that tire life is dependent on the specific pilot. Some pilots seem to impact the runway hard, which gives even less time for the upspinning of the tires, and certainly more wear on the tires. In general, it seems that tires on airliners last a few dozen trips, although the airlines don't seem to want to publicize such things. These tires are very highspeed, highloadcapacity tires, and clearly represent a major expense when they are replaced.
For practical circumstances of large airplanes, calculations suggest that it is likely that these windcatching fins can be less than 1/2 inch in width. For weight reasons, it probably could be constructed of FRP or straight fiberglass.
As soon as the airplane lowers its landing gear (generally more than fifteen seconds before touchdown), these fins would act like a child's pinwheel (or even a windspeed anemometer rotor) that would slowly start the wheel rotating. It would not represent any significant additional drag on the aircraft, so it wouldn't affect handling or safety. But, over the next fifteen seconds, each tire would spin up to a speed more suited to the plane's landing speed. Then, when the tires contacted the ground, there would be no screech and no puffs of smoke and no massive wear of the tires. A set of tires might then last a hundred times as long. Great economy would result!
Airliner tires are necessarily extremely expensive. They must be capable of supporting around 25,000 pounds on each tire, the tire must be capable of safely spinning at around 150 mph, and they MUST NOT fail under any conditions. Besides the tire being extremely expensive as a result of these requirements, mounting, balancing and testing the tires is also complicated, time consuming and expensive. Finally, the large, massive wheel/tire assembly must be mounted on the aircraft, which involves additional time and money.
Again, airlines don't seem to want to divulge the details of such things, so I am estimating that each tire on a large airliner costs $5,000 total to replace and install. For a midsized airliner, with 10 wheels, that's $50,000 each time the tires need to be replaced. If the tires last an average of 100 flights (landings, actually!), that's an expense to the airline of $500 for every landing.
If, by spinning up the wheels prior to touchdown, the wear could be reduced to 1/100 the currently accepted value, that would reduce that tire expense to $5 per landing, a savings of $495 for the airline for every single flight. This is a SIGNIFICANT saving! For this reason alone, I think there is great value in further exploring this new invention. Increasing the tire lifetime by a factor of one hundred may at first seem preposterous, but consider that, even then, the total tread lifetime would still only be about 20,000 miles, most of which was at very low speed during taxiing. Automobile tires last longer than that! This suggests that the benefits might even exceed these amazing estimates!
I would think that additional safety might occur as well, since there would not be the effect of that large instantaneous frictional drag force at the moment of contact trying to pull the nose downward when the main gear contacted the runway, and induce great stresses in the landing gear struts, as well as far less chance of a tire failure during landing that could be catastrophic.
By trying different rib curvatures at the outer edge of the disk, and different rib/scoop width, different rotational torques could be caused. By appropriate choice, it should be possible to ensure that the tires are rotating at approximately the correct rotational speed for the specific airplane. (If too tangential an angle was used, or too large a scoop size, it would actually be possible that the tires could be rotating too rapidly, and there would be a screech as the tires slowed down!)
All large commercial and military airplanes would benefit from this improvement. General aviation airplanes have lower landing speeds, and far less expensive tires, and the benefits may or may not be practical for those light aircraft.
Airlines and aircraft manufacturers have showed no interest in my letters to them. A small general aircraft company in Valparaiso, Indiana showed moderate interest for a while, but eventually lost interest when they found that the value to small aircraft was apparently minimal. Given the airlines present financial problems, I expect one or more of them to eventually show interest in my simple device that can save them many millions of dollars every year!
As to general aviation aircraft: Flying is such an expensive activity that private pilots seldom seem to worry about the cost of tire replacement. I recently heard from a pilot who got 11 years of use out of his tires, which he estimates to involve around 1650 landings. After eleven years of use, the cost of two $200 tires seems irrelevant to him! Probably true! But look! 1650 landings, at 500 feet length of actual landings, is around 160 miles of travel at any speeds greater than very slow taxiing speeds. Taxiing causes extremely minimal wear on tires, due to the very low speeds and stresses. So it could be argued that he got 160 miles of use out of a set of tires! Tires very similar to automobile tires, which we all expect to get at least 40,000 miles of high speed driving out of! Hmmmm!
So even though light aircraft do not create impressive puffs of smoke and loud screeches on landing, apparently there is still great amounts of wear due to the tire upspinning. In practical terms, there is therefore very little economic benefit of upspinning the tires on a general aviation light aircraft. But in a more theoretical sense, doesn't it seem wrong to only get 160 miles of use out of tires?
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago