The Tejas’s undercarriage Jiro Horikoshi, and the back of the envelope                          Prof. Prodyut Das 

Iss 2  

 

The Mitsubishi Zero is a legendary Japanese Fighter aircraft designed to somewhat different design concepts and thoughts. How remarkable the results were can be gauged by the fact that though it had only 60% of the  power than the Spitfire Mk V it had the same armament, more maneuverability and of course its combat range was about two times as much. Even late in the war a well-handled Zero posed a considerable threat to a Hellcat an aircraft twice as powerful and designed specifically to combat the Zero.

The key to this almost legendary performance (until they laid their hands on a flyable Zero Allied design experts could not believe the performance was possible) lay in painstaking care and attention to detail particularly in weight control. 

The purpose of this post is to show that like the Zero, with a similar dedicated painstaking weight improvement a la Jiro Horikoshi the Tejas can become quite a world class respectable warplane.

The Tejas Undercarriage

I focus on the Tejas undercarriage because I did see it (a TD series aircraft) next to a Mig 21 and the bulk of it compared to the MiG 21 left me shaking my head in disbelief. I have subsequently heard that some 400 kgs of u/c weight has been reduced by Bharat Forge. I cannot believe that with even a modicum of supervision that much excess weight could have got on to the u/c design in the first place. My earlier analyses confirms that the U/c over weight is symptomatic of the whole aircraft Whatever may be the present weight the real questions are only two:

. i)The first is have we corrected the design monitoring process by which this incredible weight was allowed to be approved in the first place. 

ii)The second is how do we know that have we reached the limit of weight reduction? Who decides that we have reached the limits and how does “he” decide that?

As described in my earlier recent blogs the present Tejas empty weight situation is comic had it not been so serious. The larger F16A block 10, with heavier engine, gun, radar is a 600 kgs lighter than the Tejas Mk1 & even the “lightened” Mk1A is heavier! Below is case study which explores how much   lighter the Tejas strut should be when compared to the MiG 21’s? The silver lining is that if we can lighten teh aircraft to the consultant's figure of 5300kgs or thereabout then we have a very serviceable combat aircraft.

Clarifying the u/c problem

The weight of the undercarriage will be not only the struts but also the wheels, jacks, brakes, tyres and the antiskid as the major components of weight. Given the 1950s- and that too Soviet - technology it is a given that these additional items in the Tejas will be considerably lighter than the MiG’s. Carbon brakes, for example, are lighter by 80- 90% from what one sees in the advertisements. The Marut even in the ‘70’s used 200 psi tyres which were lighter and used thinner (i. e. lighter) wheels than the MiG 21’s etc. ADA has no control over these items being BOC (bought out complete) and so here our focus is only on the ADA designed component – the struts.

Common sense

Common sense along with pain staking attention to detail rather than hi tech plays a very large role in the design of successful aircraft. In this case of the u/c struts it is common sense that a heavier aircraft with a higher landing speed e.g. MiG 21 would have a stronger i.e. heavier u/c than a Tejas. The MiG 21’s u/c should have been used as a bench mark by the Chief designer to set weight limits for the Landing gear team. If reports of subsequent weight reduction by Bharat Forge are true this was obviously not done.

Back of the envelope calculations

If the MiG 21’s strut’s weight is known the question is how much should the Tejas u/c weigh? It is here a quick "back of the envelope" calculation would give some indication.

At the beginning of the project the Chief designer is swamped with multiple options from which he must select the correct solutions instinctively/intuitively based on his past experience and his musings on the subject. Sometimes the Chief Designer will resort to quick “back of the envelope” calculations to check out how much he can expect. The “Back of the Envelope” is NOT precise, nor accurate nor formally acceptable but used with skill it is unbeatable as a “compass” to point in the right direction or as a gauge of the scope or set a target. I have given this rather lengthy explanation of something that is obvious because one sees from time-to-time comments by people- who obviously have never designed anything in their lives – questioning the utility of the “back of the envelope” calculations in the age of computers. Back of the envelope calculations save unimaginable amounts of time.

The “Flag Pole bending” case.

The “Funda” (old IIT UG slang) of undercarriage design is it is a “Flag Pole Bending” case or more formally a cantilever shaft with an end load. In the case of undercarriage, the “flag pole” is upside down. Dear old Roark’s “Formulas for Stress and Strain” gives the deflection of a flag pole as: a

δ = PL³ / 3 EI

δ = deflection

P = Load causing the deflection

L = Length of strut i.e. between the mounting hinge and axle

E = Young’s modulus

I = Moment of inertia

Some explanation is necessary

The aim is to have an undercarriage whose “whip” on landing is no more than a MiG 21’s whose undercarriage is of proven service. “Whip” or deflection is not an absolute standard but given the reliability of the MiG 21’s struts it is a good starting point, Deflection is a “Good enough” design parameter for this type of calculations because most items are designed not for stress as much as for deflection.

P is the load. Scientist will do enormous amounts of analysis and still come up with an over heavy undercarriage. The purpose is to find a reasonable comparison to set as a target.  The load is a function of the weight of the aircraft and the landing speed. There has been mentions of the sink rates but the sink rate IS a function of the landing speed i.e. V tan α the α being the approach angle. The designed for landing speed of the Tejas is 205 kmph (currently at 260 km. p. h. & under “concession, by an obliging IAF but 205 km.p.h. can be achieved if the weight is brought down) and that of the Bison is around 300 kmph. The MiG’s landing weight (with 25% fuel) is around 6500 kgs and the Tejas SHOULD be around 6000kg with 25% fuel remaining. We can derive a ratio from these figures (square of the landing speeds (kinetic energy) by the landing weights the MiG 21’s figures being unity.

L is the buckling length of the strut i. e. from the axle to the hinge in the fuselage. My figures is 1.3 mts for the MiG and 0.7 for the Tejas Mk1. If you have more accurate figures use them. From the above one gets the relative I (moment of inertia) and it gives you the ratio of the expected weights of the Tejas strut vis a vis the Mig 21. The Tejas u/c struts should be one-fourth the weight of the MiG 21 

I have given my figures so that interested people (not proxies, please) can contribute. If the undercarriage is lighter by the amount indicated I close my case but if the Undercarriage is heavier than the MiG 21 than there is work to be done. From my homework of comparisons, I find that the Tejas airframe should be around 2000 kg but hear that composites alone i.e. excluding the metallic parts, weigh 2450 kgs! This is criminal- as good as murder- to the aircraft and it's performance!  

Horikoshi’s rule & the symptoms of the disease.

Horikoshi wrote a book about fifty years ago “The Eagles of Mitsubishi” in which he explained how he controlled the weight of the Zero. It is worth a read because in between the lines Horikoshi explains how he studied the certification rules and “standard practice” margins he set various targets for “long parts” and increased them for short parts etc. It won’t be possible to discuss his methods in  detail but I want to cite Horikoshi’s what I would call “One lakh-th rule” as an example of the painstaking care designers have to take to seek the minimum weight. Horikoshi laid down that any component to the tune of 0.001% of the empty weight was worth the effort of re-examining for weight reduction. For the Zero this worked out to 19 gms. In the Zero even the pilot’s seat back had oblong lightening holes blanked out to save weight and yet the aircraft as remarkably strong and stood up to violent maneuvers without distress. It’s lack of battle damage resistance was not due to structural weakness in any way.

 For the LCA Mk1 Horikoshi’s rule means any component of weight over 55 gms requires a re-examination in terms of weight savings. Yes that is a lot of items but Chief designer’s must know their jobs sufficiently to be able to drop in on the hapless draughtsmen and see that the lightest weight is being achieved. That is “leading from the front” in aircraft design. My estimate is almost a ton can be removed and it would obviously transform the Tejas Mk1. The Tejas Mk1A must be viewed as a stop gap. A further ton of weight can go and it will not require much technology or time. Regarding time required to confirm how much weight savings is possible and how long it may take to confirm is it will take about 4 weeks of work  and some simple measurements using standard laboratory equipment.

A Tejas cheerleader has stated that the Undercarriage of the Tejas was indeed overweight but is now corrected. The supporter’s statement is like saying that the patient’s malaria is confined to below his knees. The overweight u/c is not a singular fault; it is the symptom of a disease- inexpert project supervision- that is plaguing the aircraft. All parts need a re-examination with respect to weight.

Where?

Where do we expect to save weight? Focus, at least at first, only one the bits designed by ADA. By my expectations these are between 70 to 100% overweight. The u/c carriage is just one example where a comparison has indicated a possibility. We should set up similar comparisons. The Mk1A  is currently at 6700 kgs and it should be around 5500-5600 kilos which was the original Dassault estimate and ,yes ,it may still be possible even with additional equipment which have been specified since then and an additional 270-280 kgs of fuel. Some facts that give hope that the projected  weight saving is possible are the following uncertainties.

i)                 There is no indication that the essential test to destruction at >100% load has been carried out. The reason seems to be that the drawings are not finalized. This, if true  is criminal incompetence as it means we do not know how much excess weight has been put on and whether the failure is due to poor detail design e,g. stress raisers or due to poor manufacturing.

ii)               Poor detail design. Composites permit us to reduce the number of parts and processes and improve finish. For example, the number of fasteners one can see on the forward fuselage is unusually numerous for a composite aircraft. They add weight and cost and spoil the performance.

iii)             Poor manufacturing. Fit, finish tolerances and lack of care in assembly and inspection can degrade performances by 8-10% in subsonic aeroplanes and even more so in Tejas class aircraft. As an example, excess Glue, a common fault in Composite aircraft does nothing but add to the weight. Has careful experiments done to see that the minimum glue is used without compromising strengths. It does not seem so. The airframe may be carrying 50 kgs or more of excess weight in terms of glue and it helps no body. As an example A 500 micron extra film of glue- i.e. 0.5 mm thick on the wings  alone will set the weight back by 88 kilos.

A close examination will raise several score of such small points. A quick comparison with other aircraft needs to be done and will indicate how much weight can still be “improved”. It is not very advanced work but it is a lot of involvement in “fiddly” work but it will transform the Tejas.

How Much…

The Dassault team concluded that teh empty weight is 5300 kilos. Even the Mk1A's empty weight of 6600 kilos is justified only if about 300 kgs of additional raw i.e. the weight of say the black boxes equipment has been added- over and above the original specifications. This is very unlikely simply because the airframe has no space to fit it in 300 kgs of avionics etc.!  .  The Tejas empty weight should be around 5600 kilos including all the equipment fitted in the Mk1 A and then some. My earlier blogs refer. In revising (mainly) the fuselage thoroughly we will not only get the weight down but also stow an additional 280 kilos of fuel internally. If we do that then the table below gives what we will get in terms of performance.

Table 1

Sl.no.	Aircraft	Empty wt.	Clean Wt.*	MTO	W/L combat wt.	Power loading	Sp. Fuel fraction	Disp. Load
1	Tejas Mk1	7280	10260	13500	277	0.75	.516	5720 kg.
2	Tejas Mk1A (2023)	6660	9640	13500	260	0.81	0.516	6340
3	Tejas Mk1 A corrected	5600	8360	13500	225	0.93	0.58	7900

·       * Full not half internal fuel.

The figures show a 40% increase in range payload with a possible ( My hunch from studying ADA's work) further 15% “bonus” on range due to peculiarities of the low AR wing. Much superior rate of energy (acceleration climb, turn rates etc) maneuvers due to the near 1;1 t/W ratio and speed and an increase in range payload by as much as 30%. This is being wasted today in dragging weight around.

Summary

The late V. Krishnamurthy can truly be said to be the father of the Indian Automotive Industry. He and his teams showed what can be done even within Government constraints. India’s Automotive Industry has gone from near zero to being the Fifth largest in the world. The same can be done for Aerospace in a much shorter time

The Indian Air Force needs to be a 50 squadron Air Force for political reasons. This is both  possible and affordable. Of these 30 squadrons will be of the improved lightened Mark 1A with weight below 6000 kgs. We are looking at an aircraft buy of perhaps 900 airframes to be produced over 15 years.

This is clearly beyond the present arrangements’ capabilities. The lacunae has been in competent management; the rest – funds, facilities, delays are often cited as reasons are actually consequences.  

The Government should form a consortium led by the Private sector where the Government would bring the Tejas “as is” as technical equity. The Private sector should audit the Tejas project technically to confirm that the weight can be brought down and the design productionized. The rest will follow. It will take two years to re-engineer the Tejas Mk1A and get it tested and ready for mass production. We have a potential winner in our hands but at present it is a sad compromise the result of prolonged neglect and bad management.  

Note 1

Though a Carrier borne fighter handicapped by the needs of an arrester hook and flotation chambers and bags the Zero had the performance to embarrass the Spitfire pilot if he was less than expert. The Zero had an empty weight of 1860 kgs compared to the comparably armed Spitfire Vb’s 2360 kgs yet had much the same armament and ammunition and about double the range. All this was achieved on an engine (Nakajima Sakae) of only 60% of the power of the Spitfire’s Merlin.

The Zero was by no means flimsy in construction and could easily withstand violent maneuvers of combat without any structural failure. What the Zero lacked was “battle damage resistance” most of it due not to structural problems as much as lack of armour protection for the pilot and self- sealing tanks for the fuel so the Zero self destructed. Western analysts have traditionally deplored this “weakness” but there is a grim sort of logic for this. Given the Zero’s spectacular range the Japanese Pilot bailing out over the jungles of Malaya or the waters of the Pacific Ocean had no chance of being recovered. It was better to improve his chances of winning the fight even at the cost of post “defeat” survival.