F-35:The $380 billion mistake

   There are two posts after this one.

See also: The F-35 is useless/ YouTube

   The F-35 is a failed program.  What is truly pathetic is that it would have been a failed program 30y ears ago.

   I will now try to explain some facts about aerodynamics and aircraft structures.

   In illustration 1, (a) represents an airfoil shape with an airflow moving past it.  The airfoil shape and its inclination cause a circular to elliptical movement of air around the airfoil.  (b) shows the addition of the circular flow to the steady air flow.  This addition causes air to flow faster over the wing, where the  speeds of the two flows add, than under the wing where they subtract.  Any flow of fluid past a surface will cause a drop in pressure on that surface; the faster the flow, the greater the pressure drop.   Since the flow is faster above the wing the pressure drop is greater over the wing and the difference in pressure, higher over the wing, lower under, causes a net pressure upward producing lift and allowing flight.

   In (c) a wedge-shaped object, similar to a fighter plane fuselage, is shown in an airflow.  Under subsonic flight it cannot produce lift, as the circulating flow would be disrupted by the back of the wedge.  There is a concept in airfoil design, known as Kutta's hypothesis, which states that at the trailing edge of an airfoil the velocity must remain finite, as in (b).  The bluff rear end of the wedge prevents this and would require an infinite fluid speed to form a circulation, therefore it can only produce lift by having a separation of flow off the top of the shape which is horribly inefficient.

   However, under supersonic conditions shockwaves, light green lines, can form producing lower pressures above and higher below to produce lift.

   The other interesting case is the wedge rotating in compressible flow.  Air blowing at 180 miles-per-hour will compress about 3 percent if brought to  a stop by a wall, the number of air molecules per cubic foot would increase by 3 percent.  The compression of air increases, roughly, as the square of the velocity.  The drop in pressure for air flowing over a surface also goes as the square of the velocity(The two phenomena are related).  For lift the increase in compressibilty gives an added bonus to the total lift.  The velocity at which air is compressibile is arguable, depending on the context, but Mach .5 (one-half the speed of sound)  is a useful approximation.  That is 370 mph at sea level and 330 mph at minimum.  Owing to the compressibility, air above that velocity is, essentially, a different fluid from low speed

   When rotating in compressible flow, a wedge, as well as an airfoil,  will produce lift from non-circulating flow.  This has in common with supersonic flow that the upper and lower surfaces are independent, Kutta's hypothesis does not apply.  Lift is produced by a vortex of air that forms over the wing or body, producing  low pressure and lift.  The faster the airfoil or body rotates, the more lift is produced. 

   In 2, the plan view of a fighter is shown.  The original wings, A, are shown as well as extended wings, B.  The most important consideration in fighter wing structures is the wing stiffness, its ability to resist bending.  There are two main types of stiffness; bending stiffness, which is the equivalent of grabbing a wing tip and trying to force it up or down; and torsional stiffness, the equivalent of grabbing the leading and trailing edges of the wing and trying to force one up and the other down.

   For bending stiffness, the wing skin provides the stiffness.  The stiffness is determined by the thickness, gage, of the wing skin multiplied by the top to bottom depth of the wing (actually, measured to the center of the skin thickness) and multiplied by a material variable known as Young's Modulus.  Young's Modulus is the force per cross-sectional area of a sample divided by its fractional elongation from the force. (For steel, a force of 30,000 lbs per square inch would produce an elongation of .001, one inch in 1000 inches, for a Young's Modulus of 30,000,000 lbs per square inch.)  This means, that for a wing, if the top to bottom depth is doubled, that the skin thickness can be reduced to half for the same stiffness.  This can be done down to a skin thickness that would cause the skin to buckle, pucker up, (2,d).  This is known as thin walled buckling.

   The idea of improving aircraft performance is to enlarge the wings from their original planform, A, and increase them to planform, B.  Now things get confusing.  Wing area and planform is measured to the centerline of the aircraft, but, as previously noted, under steady, subsonic, flight , the body cannot produce circulation and, therefor, cannot produce lift.  Only the external wing area can produce steady lift.  But, under compressible rotation the body can produce lift.  A difficulty is, that away from the wings, any reduction of pressure above the body will cause air to flow from below into the low pressure (fluids flow from high to low pressure) disrupting much  of the lift.  The same effect happens at wing tips making the ends of wings inefficient at producing lift (this is why gliders have long wings, so most of the wing produces efficient lift).

   For an F-15 the total wing area is about 550 square feet with a wingspan of about 37 feet.  For wings, area divided by span produces a number called mean (average) cord.  The wingspan divided by mean cord is the aspect ratio of the wing.  (This is also wingspan squared divided by wing area.)  The aspect ration of the F-15 is about 2.5, so the mean cord is about 15 feet.  For the F-15 the wingtip is about 5 feet long, making the centerline wing length about 25 feet.  The fuselage of the F-15 is about 12 feet wide.  So, about 260 square feet of wing is within the fuselage and about 290 square feet is external.

   For wing, B, The maximum length along the fuselage, assuming similarity to an F-15, would be about 35 feet.  With a fuselage width of 12 feet that would allow for the wing area in the fuselage to be about 420 square feet (the forward fuselage would not readily accommodate the wing extension.)  The external wing would be (35 feet + 5 feet(wingtip) = 40 feet, divided by 2,)  =20 feet average length times 25 feet (external span) = 500 square feet.  All of the numbers are about a 70% increase over the F-15 standard design.  The other limiting parameter is to not increase the total weight of the aircraft.

   Owing to the reduction in aspect ratio, the wing would not be as efficient.  The F-15 is designed to produce turning forces equal to 9 times its weight , 9g.  The larger wing could produce a higher number, I would suggest 12g would be obtainable.

   What needs to be understood is that lift is a function of atmospheric pressure and atmospheric density.  The change in pressure above and below the wing is a function of air density, but the lifting force is actually produced by air pressure.  At sea level, air pressure is about 2100 lbs per square foot.  It is half, 1050 psf, at 18 000 feet.  Air density is about one fourteenth of a lb per cubic foot at sea level an it halves at 22 000 feet.

For an F-15 wing loading, the weight of aircraft divided by wing area is around 90 psf (pounds per square foot).  For 9gs, that is 810 psf.  At 15 000 feet altitude it would be impossible to lower the pressure any more, it is impossible to create a vacuum and there is only about 1000 psf of pressure at 18 000 feet.  The only way to increase lift is to increase wing area.

   In 2b, if the wing cross section shape (wing profile) is maintained, but enlarged proportionately, for the same stiffness, the skin thickness can be decreased with the proportionate increase in cross-section length which would produce a proportionate increase in depth.  If the wing  section is twice as long, the depth at each wing position (one fourth the length, one half the length) would be twice.  The wing skin can then be one half for the same thickness to provide the same stiffness.  The wing area (twice as long but the same span ) would double, but the skin being one half as thick, would way the same.  The skin is the principal source of weight in a fighter wing to maintain stiffness.  The weight has not increased but the lift has allowing for higher turning gs.

   In 2a, the wing strip, s, owing to the reduction in efficiency from the reduced aspect ratio, would produce less lift and the center of lift would move closer to the fuselage since it is the wing tips which cause the loss of efficiency.  Both of these factors reduce the bending moment, 2c, and therefor require less stiffness.  The wing depth can remain the same and the wing can be even stiffer, or the wing skin can be reduced in thicknesss to make the wing lighter.  In addition there is something called Reynold's number which is velocity times a length divided by kinematic viscosity (the ratio of a fluid stickiness to its mass ratio).  An F-15 wing, using cord as length, has a Reynold's number of a about 100 million, twice the cord would be 200 million.  In general a thinner wing is better for higher numbers, so the wing skin thickness could be held constant and the the wing depth reduced.   Another option is to slightly extend the span while keeping the weight constant.   Additionally the cord length could be increased, which would be even more pronounced if the wing span was somewhat reduced.   Or, all of the  above could be compromised; slightly thinner, slightly more span, slightly lighter and slightly stiffer.

   The one problem is that it would fall out of the sky at low speeds and could not land, the stalling speed would be effectively raised to 300-400mph.  So, a lifting wing ,3, would have to be attached  for take-offs and landings.  A boom, similar to a refueling boom, but with 3 hinges, would attach to the fighter at its center of gravity.  The pilot would fly the two aircraft as one until they separate, at which point the lifting would fly robotically.  For connecting the boom would use laseer or radar to automatically attach when they are close enough.  If that fails, the pilot would fly his fighter with on hand while looking at a boom camera on a flat screen display and connecting the boom with his other hand.

   The landing gear would be on the wing which would save at least 1000 lbs from the fighter plus the additional structural weight need to accommodate the landing gear.  The vertical stabilizers, tails, could be moved under the fighter fuselage.  They can also be made smaller. The big vertical stabilizer is needed for low-speed flight and to have sufficient area above the turbulent flow when the plane is turning, inset 3, to maintain stability and prevent spin entry, when turning, the fuselage wake covers most of the stabilizer.  Since the fighter will never fly slowly, there is no need for large surfaces and underneath the fuselage will not place its wake on them.   However, for negative g, coming over the top of a curve, the fuselage might obscure them, so, it might be necessary to add strakes, ridges above the fuselage.  The F-16 has strakes under the fuselage to prevent spin when its tail is covered, so does the plane the Chinese claim is a stealth fighter.  The strakes provide an additional drag force to resist turning.
   In 4, the fighter is shown attached and being moved into the fixed position under the wing.  The  bending moments would be enormous, allowing for a section of boom 30 feet long and a fighter weight  of 50 000 lbs, the moment would be 1 500 000 lb-feet, it could not be generated by internal forces, so a cable, c, would have to lift and secure the fighter.  Once secured the fighter would have to be position by addition struts or bumpers, which are not shown.

  The pilot,  to resist g forces would have to be in a water-filled suit, similar to an astronaut suit with a scuba diver hood to prevent water from geysering around his neck under negative g.   The pilot would climb into his fighter and then the suit would be filled with water.