Variation is wonderful

I’m stealing a fascinating thread on Twitter from Kathleen DePlume. In some ways, it’s unsurprising: if you compound the natural variation in enough parameters, you’ll discover that everyone is unique. It’s a question of including broad tolerances, and the real question is…how broad do they have to be to accommodate 99% of humanity? And another question would be…don’t the remaining 1% deserve a place as well? The math is nifty but it isn’t the whole of human reality.

So, did you ever wonder why car seats and seatbelts are so wonderfully adjustable? It all goes back to cockpit manufacture.

The USAF wanted to make aircraft with seats and belts fitted to the “normal” airman; the tolerances weren’t too wide, but lots of fellas are normal, right?

Wrong.

As it turned out, hilariously wrong.

You see, they measured several thousand enlisted men (just men – these were the dark times before women were people) on just a few things.

Leg length, knee to ankle, hip to knee, various seat measurements. Seating height to shoulder.

Shoulder width. Arm length. Shoulder to elbow, elbow to wrist.

You get the point.

Measurements that would allow the cockpit and belts to be correct and safe, as long as they were “close enough” to the normal specifications.

So, after taking these measurements – a great undertaking, the measures got so good at it that they could do all 38* measurements in under 2 minutes – they analysed the data.

*I might be misremembering the exact number

They figured if every measurement had tolerances that fit 30% or so “normal” men, then they’d lose a few percent to the abnormally shaped weirdos (you know the ones – people whose arms are way longer than their height, or who have tiny hands compared to their feet?) they’d still fit at least 20% of their potential pilots into the custom measured Everyman cockpits, right?

Wrong.

So, so very wrong.

How many pilots do you think fit in the normal measurements on all 38 metrics?

Go on, take a guess. I’ll wait.

Actually, no I won’t, because I’m writing this as a thread.

Not a single soldier was within tolerances on all measurements.

Out of thousands and thousands of airmen measured, every last man was abnormal on at least one.

It turns out that while yes, arm length and leg length aren’t exactly independent (if you’re tall you probably have long arms AND long legs), their r-value isn’t anything like high enough for the purposes the Air Force had in mind. They’re probably long by different amounts.

So it isn’t as simple as going 0.3^38 (a number so small it should be obvious it’ll round to 0), it also wasn’t what they assumed (0.3x [almost 1]^37).

It was somewhere in between.

Okay, so where did that leave them?

It left them knowing with utter certainty that they could not design a static cockpit and recruit airmen to fit it.

They had to go the other way. Broaden the tolerances – make it so they could account for broad differences in measurements.

They had to invent adjustable seats. Adjustable straps for the safety harnesses, seats that could travel back and forth a little bit, that sort of thing.

Okay, but how does this relate to cars?

Well, there’s the obvious: once it’s been invented, why not use it in cars? But the older folk among us probably remember bench seats, and maybe even a time when you didn’t put your seatbelt on because you were insulting the driver if you did.

What changed?

Funnily enough, another clever statistician.

This one was tasked with keeping very expensive pilots alive after the Air Force had spent so much money training them up. He was supposed to be looking at the safety equipment within planes, but this was after the war, so…

…pilots weren’t actually dying in the air that much.

Mostly what killed dashing young men back in those days was car crashes.

So the statistician came back with the findings that pilots would live longer if they were forced to wear their damned seatbelts when driving.

Funnily enough, this was a huge part of the impetus to make it law that all passengers have to wear belts in cars.

It’s only sensible – but humans seldom do sensible things unless forced. And pilots are very much human.

So we all wear seatbelts now because pilots are expensive.

The moral of all this?

Mostly that maths is interesting; but also that if someone is jumping up and down demanding their right to call themself “normal”, they are full of sh*t and don’t know what they’re talking about.

Mathematically speaking.

Unfortunately, the thread lacks any mention of sources. I’d want to know a lot more about it before I could cite it as interesting history without any caveats.

1. Oggie: Mathom says

For a good example of how designing to the mean does not work, look at shoes. Wife and I both have the same bones in our feet. Our feet are not the same size (I am an 11 and 11 1/2), not the same shape (I have a really high instep and fallen arches), do not have the same toes (I have permanently crossed 3d and 4th toes and my big toe is chimping), my foot is widest at the toes but Wife’s is widest at the ball of the foot, yet, other than the width of the shoe, there is almost no variation in shoe construction.

And I am surprised. With all my study and recreational reading in history, especially modern military history (1500s to present), I have never run across the auto seat belt link. Not saying it is wrong, just never ran across it before.

2. birgerjohansson says

Also, factor in the inevitable human desire to avoid even trivial work or discomfort.
Early seat belts had to be manually adjusted. If more than one used the car, eventually the seat belts would go unused much of the time. I think it was Volvo that introduced the self-adjusting three-point belts thast are ubiquitous these days.

I can also take an example from aviation. The Mk I seat harness of the Short Stirling four-engined bomber restricted the movement of the pilots so much that many ignored regulations and kept it off.
The Stirling had a tendency to pitch nose down when flown faster that the limiting speed.
Bomber Command noticed that a lot of Stirlings crashed without any obvious cause, one of them flying almost upside down when it crashed.
.
After a lightbulb moment, a better harness was introduced and no pilot fell out of the chair when exposed to sudden turbulence again.

3. Reginald Selkirk says

Sounds unlikely to me. I would like to see some sources.

The biggest development in automobile seat belts was the three-point seatbelt. It was developed by Volvo, who has never been a big player in aviation. (Volvo derives from Latin for to roll, meanwhile that other Swedish car manufacturer derives from Svenska Aeroplan Aktiebolaget or “Swedish aircraft corporation.”

4. Snarki, child of Loki says

Not sure about the source of the “make test pilots wear car seatbelts” story, but the version I heard was that it occurred in the 50’s when the Air Force was working on going supersonic.

Horrible turbulence going from sub-sonic to super-sonic, and then THE CONTROLS REVERSE. Yeah, plenty of stuff to kill test pilots, but the cars were worse.

To address the OP: consider how you get messed up when stairs are non-standard height or depth. Some of that doubtless a “learned” response, but it’s deeply ingrained at this point.

5. acroyear says

My wife and her friends will go into long diatribes about bras over exactly this kind of thing.

6. Oggie: Mathom says

Horrible turbulence going from sub-sonic to super-sonic, and then THE CONTROLS REVERSE. Yeah, plenty of stuff to kill test pilots, but the cars were worse.

The real issue is when the aircraft is approaching the speed of sound. Airflow over parts of the aircraft will exceed Mach 1 causing compression problems which is what can reverse control surface responses. Compressibility difficulties first showed up with heavier aircraft (P-47 and P-38) with powerful engines. Both the P-47 and P-38 experienced compression problems in dives, leading to modifications to keep the aircraft slow enough. There are unverified anecdotes that P-47s exceeded Mach 1 in combat conditions, but the sound of the sonic boom could have had other sources (this being a combat area and all).

Seat belts in aircraft date back to at least WWI. As aircraft became more maneuverable, capable of inverted aerobatics, pilots realized that having something to hold them in the cockpit was important.

Development of five-point harnesses, adjustable during flight, were pretty much standard during the 1930s, though there were still difficulties.

One of the biggest hurdles in seatbelt use was convincing the pilots that yes, they would be able to exit a crashed aircraft, or exit an aircraft going down due to mechanical or battle damage issues, when they were wearing the seatbelts. Quick release buckles were developed, but some of the older pilots insisted that they were safer without the belts. I remember the exact same arguments going on in the early 1980s — older drivers insisted that not wearing seatbelts was safer as they could exit a burning vehicle, or a vehicle driven into a pond, by not wearing the seatbelt. In both cases, pointing out that it is easier to get out of a car or plane if you are conscious, but didn’t always work.

Caveat: this is from memory. Typed while listening to my twin granddaughters. And watching Peppa Pig. Produced by a nut in a manufactured facility.

7. wzrd1 says

Cute story, but I remember car manufacturers fighting tooth and nail, first against safety glass in cars, then against plain lap belts, then three point belts. Each and every safety mandate had to be shoved down their throats.

As for variation, no need to make such a study, as one could simply go to any clothier and observe off the rack variety, then note the volume of customized clothing as well.
Although, for me, there hasn’t been any variation over the course of my adult life. None at all, I simply expanded slightly faster than the universe.
And my eyes are brown for a very good reason.

8. robro says

When I was a young whippersnapper cars didn’t have seat belts at all, so there was no question of whether to wear one or not. Other than stock cars for racing (my dad built stock cars), which used a harness more than seat belts, the first standard passenger car I ever saw with a seat belt was in the mid-50s. It belonged to an uncle who along with some buddies, bought a small airplane, learned how to fly it and started a Civil Air Patrol club. He had one seat belt installed in his car for the driver. It saved him from serious injury in a bad accident, one that almost killed my 70+ yo grandfather and a cousin who were thrown from the front seat of the car.

There is one trivial question about this post that I wonder about: which war is she talking about? I would be surprised that fighter pilots in World War II weren’t using some kind of safety belt or harness, and I suspect fighter pilots in WW I would need some way to secure themselves in a plane with an open cockpit doing loops. If that’s the case, I would guess it wasn’t the USAF but the USAAF (the old Army Air Force) and/or the Navy. But then what do I know…I’m no longer a young whippersnapper.

9. wzrd1 says

Flying out of one’s seat in an aircraft hasn’t been much of a risk at all, as any dives or loops that give negative G loads tends to red out the pilot’s vision under shockingly low G loads. Pull 2 – 3 negative G’s, vision goes red from all of the blood engorging one’s eyes. Pull 5 G’s positive, it’ll be unpleasant, but loss of consciousness isn’t likely for the average person.
But, that’s for conservative, slow movements. Combat aircraft make racing and off-road vehicles look tame, as they tend to be far less stable, thereby allowing aerobatic movement and jerking forces apply. Hence, the harness, both to keep one within the confines of one’s seat and avoid slamming into the sides of the cockpit.
It’s notably difficult to fly an aircraft after you’ve broken both arms in multiple places.

But, one size does fit all, in a situation comedy.
One I saw in real life, after my father was buried in wet concrete at work up to his chest. The concrete crane bucket operator swung the bucket over his head and yelled for him to grab on, before another retaining wall collapsed, which he did. He was pulled from the concrete naked, his clothing ripped from him. So, he arrived home wearing borrowed clothing around two sizes too small, with a rope for a belt.
The laughter relieving the horror that he was nearly crushed to death under the under installation airport fuel farm. His crew, noticing what was happening slightly earlier ran from the hole – on top of the wet concrete. Completing a comic moment that was nearly a tragedy.
Capping it all, him threatening his accompanying him home crew with being beaten bloody if they don’t come in for some coffee, as they were Black and it was the 1960’s. Obviously, they came in and enjoyed some snacks.
No neighbors complained, as the neighborhood was predominantly Jewish and had living memory of misfortune and prejudice from Germany.
Well, that and you really don’t want to piss off an old 2nd Division Marine former boxer and guy who slings 20 yards of concrete manually on a daily basis. ;)

10. says

My command didn’t have records to confirm or deny the OP, but the OP is consistent with other records that it did have. In particular, my command (and, as the command historian, my office) DID have records related to how issued large-aircraft flight suits were to be sized, which included one memorable ten-or-twelve-page paper from the 1960s objecting that making sleeves long enough to fully cover the arms of those with abnormally-long arms would impair military appearance and possible lead to problems with bunching at the elbows for those with shorter arms, so arm length needed to be one of the adjustable options for standard-issue flight suits. This was folded into a budget request, so it ended up in my office…

And a couple of other comments:

@4 Volvo had an aviation division essentially from day one. Aviation has used subcontractors for certain discrete subsystems since the 1930s — that is, when significant factory/production line concepts from the automobile industry became fully integrated. (Even as late as 1944, most non-US aircraft were more than 50% hand-assembled in a single spot on the floor, with nothing resembling the production line of Ford Automotive.) More to the point, Volvo was a major component contributor to the Drakken, formally manufactured “by” Saab starting in the 1950s.

@6 Yes, it’s a lot easier to exit a crashed vehicle when not wearing a seatbelt. Indeed, most of those who do so do it during the crash… and don’t even make it to the ER to become statistics amenable to articles from lazy journalists.

@8 You really don’t want to know about the economic arguments made against safety gear in automobiles and aircraft (and even watercraft) over the years, all of which boil down to “It will cause a small price increase to the end user and that would be bad and reduce our sales.” Just remember that the only production automobile with an afterburner was the Ford Pinto, because internal memoranda convinced management that consumers would buy fewer Pintos if the base cost of a vehicle as offered to the public exceeded \$2,000 — a figure demanded by Lee Iacocca for Reasons. And the profit margin would have been shaved below the demanded percentage by adding the (from memory) approximately \$8 to manufacturing costs to re-site the gas tank and extend an already-existing flange to completely cover its lower rear quarter.

That most of these economic arguments were themselves based upon flawed data (this is how much it would cost to substitute currently-manufactured, low-volume, hand-finished components for our regular production-line stuff) escaped regulators until the pushback against mandatory installation of airbags in automobiles. At least in the US, aviation largely avoided this problem because everybody believed they needed to comply with milspec requirements (for eligibility and prestige even if not for actual contracts), so as soon as a military specification for “an” aircraft system included feature X the industry whinged and followed along regardless (taking advantage of cost-plus contracting).

11. Allison says

The first time I ever saw a seatbelt in a car was in the mid-1960’s, when my mother bought a VW bus. As I recall, US cars did not have seat belts, but many? most? European cars did. I don’t know whether there were laws mandating it or if the European car companies were simply slightly more sensible (= less bloody-minded) than the US ones. I tend towards the latter explanation because the US car manufacturers are to this day extremely unwilling to let reality affect how they do things, even when they’d have to do so just to survive.

12. hillaryrettig1 says

years ago, heard a story about how there was an air force base where, as you were exiting, there was a sign saying “You are about to engage in man’s most dangerous activity,” or similar. It was referring to driving on a highway.

google didn’t turn anything up, but maybe someone else on the thread can confirm.

13. robro says

Jaws @ #11 — “You really don’t want to know about the economic arguments made against safety gear in automobiles and aircraft”. You want to hear even less about the fashion arguments against safety gear in automobiles a la “The belt will wrinkle my clothes.” I recall seeing PSAs in the early days of seatbelts comparing the effect of seatbelts on clothes versus the effect of an accident on your appearance.

14. robro says

PS to #14—There should be “a don’t want to hear” in there.

15. Oggie: Mathom says

suspect fighter pilots in WW I would need some way to secure themselves in a plane with an open cockpit doing loops. If that’s the case, I would guess it wasn’t the USAF but the USAAF (the old Army Air Force) and/or the Navy.

United States Army Signal Corps, which spun off aircraft as the United States Army Air Service which became the US Army Air Corps in 1926, which became the US Army Air Forces in 1941.

And doing loops is not the problem — as noted by wzrd-1. Flying inverted or doing an outside loop (partial outside loops were used by some fighter pilots in WWI to shake off an enemy on their tail) or nosing over will create negative gees in the cockpit. Mostly, though, seat belts just kept the pilot where he could reach the pedals, stick, throttle, spark retarder, and gun switch.

16. Oggie: Mathom says

I would guess it wasn’t the USAF but the USAAF (the old Army Air Force) and/or the Navy.

United States Army Signal Corp had the aircraft. They spun off the US Army Air Service as a separate part of the Signal Corp. Then, in 1936, the USAAS became the US Army Air Corp. In 1941, the US Army Air Forces were created as a separate command within the US Army. So, USAAS to USAAC to USAAF to USAF.

Navy aviation started with the Bureau of Navigation (US Navy) ion 1911, which later became the United States Naval Flying Corps and the Naval Reserve Flying Corps. The US Navy Bureau of Aviation dates to 1921, and they defeated repeated attempts by the various US Army air organizations to take over Naval aviation. And, as far as I can tell from my sources, almost all of the aircraft used by these organizations had seat belts. A photo of E. B. Ely, who flew a Curtiss Model D off of the USS Birmingham back in 1911 shows him wearing a seat belt — though it is attached to the seat back, not the seat base, so a sudden deceleration event would have caused severe internal injuries.

Bunch of damn wing wipers.

years ago, heard a story about how there was an air force base where, as you were exiting, there was a sign saying “You are about to engage in man’s most dangerous activity,” or similar. It was referring to driving on a highway.

When I was in Basic at Fort Lost in the Woods, Misery, I volunteered for the two hour course to become a driver, light vehicle. I much preferred driving to riding in the back of a pickup truck. Our company’s Chevy Cheyenne pickup had a nicely made sign on the dashboard: “You are now engaged in the most dangerous activity in the US Army. Don’t add to it.”

17. says

Since speed, cars and deaths are in the same story… The 24 Heures Du Mans happened a month ago. Drivers race in teams of three. Endurance racing pitstops are much longer (1-2 minutes) than in “sprint” racing (e.g. F1, Nascar) for safety reasons (e.g. the engine is turned off and no one touches the car while refueling).

Driver changeovers happen during pitstops. Each driver has a different body, and they don’t have time to swap the seats. So they build the seat for the largest driver and use inserts behind or under the other drivers so that the seat, wheel, and pedal positions don’t have to change. The four or six point seatbelts release and adjust much like airplane seats, so a custom fit isn’t necessary.

18. whheydt says

I’m also one of those that remember cars without any seat belts. FIrst car my parents had with seat belts was a 1966 Dodge A100 van. It’s the car I learned to drive in. Parallel parking was a breeze because it only had a 90″ wheel base. Before taking the on-the-road driving test (California), I set out two garbage cans to practice parking between them. Turned out that the space the DMV used was about twice as big. (The real reason for either parallel parking or doing a 3-point turn was to demonstrate that you could properly control the vehicle going backwards. I got about half way through parking when the tester to me to just go ahead and not bother completing parking.)

19. Oggie: Mathom says

I got about half way through parking when the tester to me to just go ahead and not bother completing parking.

Same thing happened to me. I was taking my driving test in my 1967 VW Beetle. I think he just wanted to get out of the car. Hagerstown, MD in 1983.

20. EigenSprocketUK says

The Real Engineering yewtoob channel has an interesting video about seatbelts, the first portion of which talks about earliest designs and then Volvo’s role in the development towards three point belts. Later there’s more focus on the mechanisms of intertial locking, heading for pretensioners. Not so much aviation in there, though.

21. John Morales says

Sez Wikipedia: “Seatbelts were invented by English engineer George Cayley, to use on his glider, in the mid-19th century.”

In passing, regular belts were invented somewhat earlier, and are also adjustable.

22. Gordon Davisson says

This sounds a lot like a study Gilbert Daniels did for the Air Force in 1952, but that was for flight suits, not seats. Matt Parker (of “Stand-up Maths”) has an excellent video about it: https://www.youtube.com/watch?v=NbiveCNBOxk, and he has links to scans of the study (and a callout to Caroline Criado Perez’s book “Invisible Women”, about the additional problem of assuming all people are men).

Here’s an excerpt from the study results:

The fallacy of the “average man” concept is further illustrated by a study based on body measurements made on over 4,000 Air Force flying personel. From a total of 132 available measurements a smaller group, all useful in clothing design was selected. (Measurements applicable to other problems such as cockpit layout or seat design could equally well have been chosen; they would have given much the same results). The records of the 4,000-plus men were then examined to see how many of these men, if any, could be considered average in all of the selected measurements.

[…]

1- of the original 4063 men
1055 were of approximately average stature
2- of these 1055 men
302 were also of approximately average chest circumf[erence]
3- of these 302 men
143 were also of approximately average sleeve length
4- of these 143 men
73 were also of approximately average crotch height
5- of thee 73 men
28 were also of approximately average torso circumf[erence]
6- of these 28 men
12 were also of approximately average hip circumfer[ence]
7- of these 12 men
6 were also of approximately average neck circumf[erence]
8. of these 6 men
3 were also of approximately average waist circumfer[ence]
9- of there 3 men
2 were also of approximately average thigh circumfer[ence]
10- of these 2 men
0 were also of approximately average in crotch length

23. John Morales says

[The things one learns!]

“Crotch length is the length from the top of center front in between your legs to the top of center back. Crotch point is at the bottom of the pelvic floor and is where the front crotch curve and back crotch curve meet.”

24. Rich Woods says

…pilots weren’t actually dying in the air that much.

Mostly what killed dashing young men back in those days was car crashes.

This reminds me of meeting a friend’s brother, way back in the 1980s. The brother was an RAF pilot who flew Tornados and had many stories to tell of his and his colleagues’ experiences practicing nap-of-earth flying, 250mph at an altitude of 250ft or lower, the idea being to stay under the enemy’s radar until in a position to attack it. Turns out the man was a speed junky and drove his car the same way, but without the advantage of highly-advanced terrain-following avionics. The tales he told of him and his mates getting drunk and driving like fucking idiots around the country lanes near his RAF station convinced me that if the Cold War went hot half our attack squadrons would be found in the hospital or the jail rather than on standby.

25. says

@25

This is getting a bit off-topic, but: You were doing just fine until the last line.† The pilots (RAF or USAF) would not have been in jail — there was a cultural thing such that a pilot otherwise nailed for intoxication (driving or otherwise) was released by the constabulary to the gentle custody of the colonel/group captain, or higher, next up in the chain of command, unless there was grievous bodily harm involved. Jail was reserved for the enlisted swine and those officers who didn’t have wings on the left pocket (except maybe Col Lawrence, who might have lived longer had he been jailed for one of his prior motorcycling-while-drunk stunts).

Needless to say, this caused some heartburn, especially around places like RAF Coltishall when [redacted for privacy], and RAF Upper Heyford virtually every month. (Not at all coincidentally, the USAF F-111 — another nape-of-earth-on-special-autopilot aircraft — was the primary aircraft assigned to Upper Heyford at the time.)

† I spent several nervous Cold War years stationed in England, mostly as a commanding officer of “non-flying” units like rather large enlisted-heavy aircraft maintenance squadrons.

26. Jazzlet says

The ones that ended up in hospital were NOT popular, I’ve a cousin who worked on the wards they ended up in for a time, there were the “what do you call a pilot from an American airbase?” “organ doner” jokes which were partly down to their relative lack of experience with alcohol – the legal drinking age in pubs being 18 over here natives have usually got it out of their system at similar ages – and the feeling that they were taking up beds that ought to have been used by locals with real needs. However they were also considered arrogant and entitled, which resulted in an unwritten rule that whenever they buzzed for help they were automatically put to the back of the queue of things the nurses needed to do.

27. mathscatherine says

“…pilots weren’t actually dying in the air that much.

Mostly what killed dashing young men back in those days was car crashes.”

My Father-in-law spent many years in the band for the RAAF (Australian Air Force). Every time a member of the air force dies, the official band plays at their funeral – so he tends to find out what kills them. The answer nowadays is mostly motorcycle crashes.

(As an aside – how do I do that nice quoting thing? @25 for example? Thank you)

28. John Morales says

mathscatherine, HTML blockquote, thus
<blockquote>`chunk of text`</blockquote>

29. wzrd1 says

John Morales @ 24, there is a relationship in average on pelvis size and leg length. Something about chemical messengers and whatnot.
Lest we all end up with mile long legs and asphyxiate once able to stand. ;)

30. Buck Webb says

I found a copy of “The Human Body in Equipment Design” at a booksale which summarizes the military body data. It also has a nice chapter on preventing injury which describes experiments dropping human cadaver heads onto concrete from various heights to study fracturing and brain compression for helmet and maximum acceleration requirements.

31. Buck Webb says

I found a copy of “The Human Body in Equipment Design” at a booksale which summarizes the military body data. It also has a nice chapter on preventing injury which describes experiments dropping human cadaver heads onto concrete from various heights to study fracturing and brain compression for helmet and maximum acceleration requirements.

32. wzrd1 says

Dropping human cadaver heads onto concrete? Sounds expensive. Second Lieutenants are cheaper.
Seriously though, that’s one starting point, but there is a significant difference in strength in cadaver bone and living bone as the proteins degrade and the bone becomes stiffer and less resilient.
Still, it’s better than other testing I’ve read about, such as testing helmets with living chimpanzees wearing them. Talk about wrong applications and cruelty!
Thankfully, we have much better models to work with now. And an excess of second lieutenants…
Privates being utterly useless, as their heads are just way too hard.

Oh, due to information learned from the Challenger disaster, NASA redesigned the astronauts helmets, as the version used in the disaster apparently resulted in significant injuries to the astronauts.

33. felixd says

An outstanding example of the “curse of dimensionality” for high-dimensional Gaussian probability distributions. This would happen for any instance where a many-parameter system is designed around typical values for each parameter.
https://bbabenko.github.io/harry-potter/