CIDCrazyJay
Well-Known Member
Design Loads
Most light aircraft structures are designed to clearly defined limit and ultimate load requirements.
These well known categories are often cited by pilots, designers, and enthusiasts alike.
But is anyone aware of a rational basis for these requirements?
Can anyone point to the thought process, or any mathematical derivation to arrive at these seemingly arbitrary numbers?
What is the source, having a scientific engineering basis?
These category and limits are:
Normal: +3.8g/-1.52g
Utility: +4.4g/1.76g
Aerobatic: +6g/-3g
Transport: Special case derived from a formula. But "need not exceed 3.8g" is part of the verbiage. Why must "normal" category airplanes meet the 3.8g requirement, but ALL part-25 passenger carrying transports are capped at a load factor at, or under this same limit load?
These numbers are often taken as gospel, but I do not subscribe to the idea that blind acceptance is a completely rational, or even reasonable assumption.
For example: A well flown loop requires at least 3g but often 3.5-4g at the initiation to ensure plenty of energy is carried into the vertical to complete it. An aerobatic aircraft designed to the above specifications is incapable of safely performing an outside loop.
Is an aircraft really "aerobatic" if basic outside-looping maneuvers are prohibited?
________________________
Moving forward:
In the name of simplification, let's just focus on one case: Normal category, positive load factor, +3.8g.
Where did this number come from?
Is it arbitrary?
I've been attempting to determine on what basis we can arrive at this highly-specific decimal number.
I've partially ruled-out human factors. As these limits have been known since at least as early as 1929, an early NACA report stated a pilot sustained in excess of 10.5g. Source: https://ntrs.nasa.gov/api/citations/19930091375/downloads/19930091375.pdf
USAF design requirements for many decades were +7.33g limit load, +11g ultimate. Many notable fighters from the period between 1940-1960s accepted this criteria, when flown at a certain gross weight. The T-38 included.
This was indeed a rational specification, as it accounted for the generally accepted threshold that sustained +7g load factor would cause loss of consciousness, and the above proven fact a highly determined pilot could momentarily endure at least +10.5g.
Combined with the established Ultimate/Yield strength-ratio of aluminum; the primary structural material.
Aluminum, 2024-T3:
Tensile Strength: 63ksi
Tensile Yield: 42ksi
Fatigue limit: 20ksi.
63/42 = 1.5 safety factor.
Another consideration:
[11g*(20ksi/63ksi)]= 3.5g fatigue limit. This allows nearly unlimited loops, pull-ups, and routine overhead-breaks.
Excessive G-loads above this fatigue threshold have an exponentially detrimental effect on airframe lifespan.
So, let's reverse engineer the FAA normal category limit load factor: 3.8g * 1.5 = 5.7g
This is far, far below what a human can endure, and is also below what ordinary people can readily sustain. Therefore, this might not have been a factor for the FAR load requirement.
Unless, perhaps it was selected based on wooden aircraft designs of that era:
Sitka Spruce:
Modulus of Rupture: 10.2ksi.
Compression Strength: 5.5ksi.
Yield Strength: None per se, so long as compression-cracks are avoided. (5ksi).
10.2/5.5 = 1.85
3.8g * 1.85 = 7g
Note: 7g was the classically accepted limit for consciousness, in both WWI and WWII into the Vietnam era. Above 6g, grey-out is a regular phenomenon. So, perhaps designers of civil aircraft of the 1930s had simply selected 7g as the ultimate load, and this naturally resulted in a limit-load of 3.8g for their wood construction methods.
And, perhaps the FAA simply wrote that code in ink. Then applied the 3.8g limit load to aluminum with an ultimate tensile to yield strength ratio of 1.5.
3.8*1.5 = 5.7g.
This is somewhat less arbitrary than selecting 5.7g out if thin air for an ultimate load; since anyone up to perhaps 80 years old, with or without a pacemaker, can readily remain conscious up to, and beyond this point with no special training or technique.
Now: For aluminum structures, What is the fatigue limit?
3.8*(20ksi/42ksi) = 1.81g
Most civil airplane flights probably remain below this limit. Or do they? What bank-angle corresponds to 1.8g?
-cos(1/1.8) = 56.25 degrees.
(Assumption: Coordinated, steady-state, non-descending turn conducted in still-air, at the specified bank angle).
This is a strange, sort of no-mans land, seemingly arbitrary fatigue limit. Where do we find regular bank angles near this?
The answer might be found in the FARs: Aerobatic Maneuvers are defined as "a bank angle exceeding 60 degrees", among other conditions. https://www.ecfr.gov/current/title-14/chapter-I/subchapter-F/part-91/subpart-D
Therefore; Logically: Normal category aircraft may be operated up to, but not exceeding 60 degrees of bank.
[1/(60cos)] = 2.0g
2g/20ksi fatigue strength = 10ksi per g. ...Multiplied by 42ksi = 4.2g limit load.
This 4.2g limit load would clearly be a rational basis for all "Normal" category airplanes, which are legally permitted to operate up to 60 degrees of bank, corresponding to 2.0g. This also seems like a more optimal design point for new aluminum E/AB designs; because it slots into the gap between the 3.8 & 4.4g of the more durable Utility category. (Which has a fatigue load limit of 2.1g).
Perhaps the FAA "Utility" category +4.4g, was in fact derived from this 60-degree bank angle assumption, then simply given a +0.1g tolerance over the assumed 2.0g fatigue limit. Or, perhaps it was simply derived by taking 6g, plus 10% for the normally accepted human grey-out/blackout limit.
Who knows?
This still leaves the question, why a 3.8g limit load? And was a 1.8g fatigue limit threshold even a factor? Shouldn't it be?
See the FARs again, to determine how people might be using "normal category" airplanes up to, but not exceeding 1.8g on a regular basis: Specifically, check the airman performance standards. Here we find private pilots must demonstrate (and therefore practice) "steep turns" of 45, Plus or minus 5 degrees of bank.
45 degrees = 1.42g
50 degrees = 1.56g
...What about 1.81?
Check the standards for commercial ticket: 50 degrees, plus or minus 5:
55 degrees = 1.75g.
Again, 1.81g fatigue limit load = 56.5 degrees.
So, perhaps the limit-load regulation is derived from the fact commercial student pilots often practice 50+/-5 degree steep turns? This limit load provides plenty of margin for the Private pilot, who is expected to perform at 45 degrees, and always remain below 50 degrees. With the assumption that most commercial License prospects can probably fly precisely enough, at this juncture in their training program, to remain within 5 degrees of 50, just below the 56 degree mark.
Or, perhaps these airman standards are themselves derived from the fatigue limit loads of a 3.8g aluminum airplane. In any case, it appears to me that the 3.8g limit load is indeed a true "minimum" requirement.
For ordinary airplanes, which are legally allowed to operate at up to 60 degrees of bank, flown by people who can easily survive and operate an aircraft at or above 6g:
It would seem that a 2.0g fatigue, 4.2g limit load, with a 6.3g ultimate, is a far more desirable design point.
This would provide 6g of load factor (+5%) for a pilot to get out of upsets, botched spin recoveries, flight into IMC, severe gusts, or inadvertently entering a downwind-rotor.
For those who disagree, that is certainly fine: But think about this, it now opens up new possibilities for designs utilizing a spruce spar, and other wooden aircraft: Take your own accepted 5.7g ultimate load, and divide by 1.85 of the compression strength/modulus of rupture ratio, and you arrive at 3.4g limit load. And a conservative 3.0g would then be (approximately) the safe "fatigue limit" to avoid any chance of compression-cracks over time: Therefore, it has the exact same ultimate strength, yet far better fatigue properties at regular everyday (<3.4g) loadings of an ordinary "normal category" aluminum airplane.
This would save quite a bit of weight at the exact same practical strength limit.
By lowing the wooden wings ultimate load factor from 7.0 down to the previously accepted 5.7g, this would still provide greater long-term durability over aluminum with a higher limit load.
(This would not be my personal choice). ~ But it is a rational one, once the published, somewhat arbitrary 5.7 ultimate load factor is taken as gospel truth.
--------------------------
As to some other design cases, perhaps these limits are unnecessarily high?
Take Part-103 aircraft, AKA "ultralights" for an example.
Legal requirements:
Stall Speed: 24kt
Maximum speed: 55kt
(55/24)^2 = 5.25g
These aircraft, assuming this simplification, are incapable of exceeding 5-1/4g load while at maximum level flight speed, near sea-level.
5.25/1.5 safety factor = 3.5g limit load.
This might be considered a reasonable, rational, and perfectly adequate minimum design point for this specific type of aircraft.
________________________
Logically, this can be taken further: In fact, any arbitrary aircraft design can be worked backward from this basic, conservative assumption:
Cessna 172 S
Max gross weight 2,550lb.
Limit/Ultimate load 3.8/5.7g.
VS clean = 53kt
Max Horizontal speed, full power, at sea level = 126ktas.
(126/53)^2 = 5.65g
This is just below the published ultimate load factor of 5.7g. Therefore, this airplane is unlikely to suffer structural failure at any speed inside the normal operating range. This is probably why, despite 15,000 of them being produced, with many being used as trainers, by low time pilots, and in rental fleet service; they suffer almost zero major structural failures.
Another way of saying this: (CLmax/ultimate load factor) = minimum acceptable CL at Vh.
Calculate dynamic pressure (q) at Vh (max level flight speed). Multiply by the above minimum lift coefficient. Select this wing loading at max gross weight. And you have an airplane with a V-N diagram where total structural failure will probably never happen at any speed below maximum speed in level flight. No. Matter. What.
Cessna knew what they were doing to make their brilliantly conceived, reasonably safe, endlessly practical airplane.
_______________________
The intent of this rambling, is to provoke some thought into these topics, instead of making simplified assumptions about what is acceptable, and what is not.
Every new aircraft design should be entirely derived from a logical and rational basis. Instead of being painstakingly and meticulously designed to a completely arbitrary, unsubstantiated, decimal-place number. One which was simply inked onto a page by a bureaucratic organization that is either unwilling, or otherwise incapable of providing the derivation or rationale for their seemingly arbitrary decree, no mater how well it was conceived.
Those folks who derived it way back when, have probably long since passed. It might just be that some of their historic assumptions do not hold water for unique categories, such as Part-103.
Nor should they always be applied in this age of high-tech materials, expanding performance, and ever-changing technology.
IMO... Most aluminum E/AB airplanes designed to only 3.8g, or composite airplane having an ultimate load/limit load factor less than 4; If either is to be built by amateurs, should probably be viewed with some level of skepticism until it is proven in practice with some level of statistical significance.
It seems as if many designers and builders agree, as quite a few popular kits out there are designed to higher than minimum load limits. With this feature being cited somewhat frequently.
This might make a good poll.
Most light aircraft structures are designed to clearly defined limit and ultimate load requirements.
These well known categories are often cited by pilots, designers, and enthusiasts alike.
But is anyone aware of a rational basis for these requirements?
Can anyone point to the thought process, or any mathematical derivation to arrive at these seemingly arbitrary numbers?
What is the source, having a scientific engineering basis?
These category and limits are:
Normal: +3.8g/-1.52g
Utility: +4.4g/1.76g
Aerobatic: +6g/-3g
Transport: Special case derived from a formula. But "need not exceed 3.8g" is part of the verbiage. Why must "normal" category airplanes meet the 3.8g requirement, but ALL part-25 passenger carrying transports are capped at a load factor at, or under this same limit load?
These numbers are often taken as gospel, but I do not subscribe to the idea that blind acceptance is a completely rational, or even reasonable assumption.
For example: A well flown loop requires at least 3g but often 3.5-4g at the initiation to ensure plenty of energy is carried into the vertical to complete it. An aerobatic aircraft designed to the above specifications is incapable of safely performing an outside loop.
Is an aircraft really "aerobatic" if basic outside-looping maneuvers are prohibited?
________________________
Moving forward:
In the name of simplification, let's just focus on one case: Normal category, positive load factor, +3.8g.
Where did this number come from?
Is it arbitrary?
I've been attempting to determine on what basis we can arrive at this highly-specific decimal number.
I've partially ruled-out human factors. As these limits have been known since at least as early as 1929, an early NACA report stated a pilot sustained in excess of 10.5g. Source: https://ntrs.nasa.gov/api/citations/19930091375/downloads/19930091375.pdf
USAF design requirements for many decades were +7.33g limit load, +11g ultimate. Many notable fighters from the period between 1940-1960s accepted this criteria, when flown at a certain gross weight. The T-38 included.
This was indeed a rational specification, as it accounted for the generally accepted threshold that sustained +7g load factor would cause loss of consciousness, and the above proven fact a highly determined pilot could momentarily endure at least +10.5g.
Combined with the established Ultimate/Yield strength-ratio of aluminum; the primary structural material.
Aluminum, 2024-T3:
Tensile Strength: 63ksi
Tensile Yield: 42ksi
Fatigue limit: 20ksi.
63/42 = 1.5 safety factor.
Another consideration:
[11g*(20ksi/63ksi)]= 3.5g fatigue limit. This allows nearly unlimited loops, pull-ups, and routine overhead-breaks.
Excessive G-loads above this fatigue threshold have an exponentially detrimental effect on airframe lifespan.
So, let's reverse engineer the FAA normal category limit load factor: 3.8g * 1.5 = 5.7g
This is far, far below what a human can endure, and is also below what ordinary people can readily sustain. Therefore, this might not have been a factor for the FAR load requirement.
Unless, perhaps it was selected based on wooden aircraft designs of that era:
Sitka Spruce:
Modulus of Rupture: 10.2ksi.
Compression Strength: 5.5ksi.
Yield Strength: None per se, so long as compression-cracks are avoided. (5ksi).
10.2/5.5 = 1.85
3.8g * 1.85 = 7g
Note: 7g was the classically accepted limit for consciousness, in both WWI and WWII into the Vietnam era. Above 6g, grey-out is a regular phenomenon. So, perhaps designers of civil aircraft of the 1930s had simply selected 7g as the ultimate load, and this naturally resulted in a limit-load of 3.8g for their wood construction methods.
And, perhaps the FAA simply wrote that code in ink. Then applied the 3.8g limit load to aluminum with an ultimate tensile to yield strength ratio of 1.5.
3.8*1.5 = 5.7g.
This is somewhat less arbitrary than selecting 5.7g out if thin air for an ultimate load; since anyone up to perhaps 80 years old, with or without a pacemaker, can readily remain conscious up to, and beyond this point with no special training or technique.
Now: For aluminum structures, What is the fatigue limit?
3.8*(20ksi/42ksi) = 1.81g
Most civil airplane flights probably remain below this limit. Or do they? What bank-angle corresponds to 1.8g?
-cos(1/1.8) = 56.25 degrees.
(Assumption: Coordinated, steady-state, non-descending turn conducted in still-air, at the specified bank angle).
This is a strange, sort of no-mans land, seemingly arbitrary fatigue limit. Where do we find regular bank angles near this?
The answer might be found in the FARs: Aerobatic Maneuvers are defined as "a bank angle exceeding 60 degrees", among other conditions. https://www.ecfr.gov/current/title-14/chapter-I/subchapter-F/part-91/subpart-D
Therefore; Logically: Normal category aircraft may be operated up to, but not exceeding 60 degrees of bank.
[1/(60cos)] = 2.0g
2g/20ksi fatigue strength = 10ksi per g. ...Multiplied by 42ksi = 4.2g limit load.
This 4.2g limit load would clearly be a rational basis for all "Normal" category airplanes, which are legally permitted to operate up to 60 degrees of bank, corresponding to 2.0g. This also seems like a more optimal design point for new aluminum E/AB designs; because it slots into the gap between the 3.8 & 4.4g of the more durable Utility category. (Which has a fatigue load limit of 2.1g).
Perhaps the FAA "Utility" category +4.4g, was in fact derived from this 60-degree bank angle assumption, then simply given a +0.1g tolerance over the assumed 2.0g fatigue limit. Or, perhaps it was simply derived by taking 6g, plus 10% for the normally accepted human grey-out/blackout limit.
Who knows?
This still leaves the question, why a 3.8g limit load? And was a 1.8g fatigue limit threshold even a factor? Shouldn't it be?
See the FARs again, to determine how people might be using "normal category" airplanes up to, but not exceeding 1.8g on a regular basis: Specifically, check the airman performance standards. Here we find private pilots must demonstrate (and therefore practice) "steep turns" of 45, Plus or minus 5 degrees of bank.
45 degrees = 1.42g
50 degrees = 1.56g
...What about 1.81?
Check the standards for commercial ticket: 50 degrees, plus or minus 5:
55 degrees = 1.75g.
Again, 1.81g fatigue limit load = 56.5 degrees.
So, perhaps the limit-load regulation is derived from the fact commercial student pilots often practice 50+/-5 degree steep turns? This limit load provides plenty of margin for the Private pilot, who is expected to perform at 45 degrees, and always remain below 50 degrees. With the assumption that most commercial License prospects can probably fly precisely enough, at this juncture in their training program, to remain within 5 degrees of 50, just below the 56 degree mark.
Or, perhaps these airman standards are themselves derived from the fatigue limit loads of a 3.8g aluminum airplane. In any case, it appears to me that the 3.8g limit load is indeed a true "minimum" requirement.
For ordinary airplanes, which are legally allowed to operate at up to 60 degrees of bank, flown by people who can easily survive and operate an aircraft at or above 6g:
It would seem that a 2.0g fatigue, 4.2g limit load, with a 6.3g ultimate, is a far more desirable design point.
This would provide 6g of load factor (+5%) for a pilot to get out of upsets, botched spin recoveries, flight into IMC, severe gusts, or inadvertently entering a downwind-rotor.
For those who disagree, that is certainly fine: But think about this, it now opens up new possibilities for designs utilizing a spruce spar, and other wooden aircraft: Take your own accepted 5.7g ultimate load, and divide by 1.85 of the compression strength/modulus of rupture ratio, and you arrive at 3.4g limit load. And a conservative 3.0g would then be (approximately) the safe "fatigue limit" to avoid any chance of compression-cracks over time: Therefore, it has the exact same ultimate strength, yet far better fatigue properties at regular everyday (<3.4g) loadings of an ordinary "normal category" aluminum airplane.
This would save quite a bit of weight at the exact same practical strength limit.
By lowing the wooden wings ultimate load factor from 7.0 down to the previously accepted 5.7g, this would still provide greater long-term durability over aluminum with a higher limit load.
(This would not be my personal choice). ~ But it is a rational one, once the published, somewhat arbitrary 5.7 ultimate load factor is taken as gospel truth.
--------------------------
As to some other design cases, perhaps these limits are unnecessarily high?
Take Part-103 aircraft, AKA "ultralights" for an example.
Legal requirements:
Stall Speed: 24kt
Maximum speed: 55kt
(55/24)^2 = 5.25g
These aircraft, assuming this simplification, are incapable of exceeding 5-1/4g load while at maximum level flight speed, near sea-level.
5.25/1.5 safety factor = 3.5g limit load.
This might be considered a reasonable, rational, and perfectly adequate minimum design point for this specific type of aircraft.
________________________
Logically, this can be taken further: In fact, any arbitrary aircraft design can be worked backward from this basic, conservative assumption:
Cessna 172 S
Max gross weight 2,550lb.
Limit/Ultimate load 3.8/5.7g.
VS clean = 53kt
Max Horizontal speed, full power, at sea level = 126ktas.
(126/53)^2 = 5.65g
This is just below the published ultimate load factor of 5.7g. Therefore, this airplane is unlikely to suffer structural failure at any speed inside the normal operating range. This is probably why, despite 15,000 of them being produced, with many being used as trainers, by low time pilots, and in rental fleet service; they suffer almost zero major structural failures.
Another way of saying this: (CLmax/ultimate load factor) = minimum acceptable CL at Vh.
Calculate dynamic pressure (q) at Vh (max level flight speed). Multiply by the above minimum lift coefficient. Select this wing loading at max gross weight. And you have an airplane with a V-N diagram where total structural failure will probably never happen at any speed below maximum speed in level flight. No. Matter. What.
Cessna knew what they were doing to make their brilliantly conceived, reasonably safe, endlessly practical airplane.
_______________________
The intent of this rambling, is to provoke some thought into these topics, instead of making simplified assumptions about what is acceptable, and what is not.
Every new aircraft design should be entirely derived from a logical and rational basis. Instead of being painstakingly and meticulously designed to a completely arbitrary, unsubstantiated, decimal-place number. One which was simply inked onto a page by a bureaucratic organization that is either unwilling, or otherwise incapable of providing the derivation or rationale for their seemingly arbitrary decree, no mater how well it was conceived.
Those folks who derived it way back when, have probably long since passed. It might just be that some of their historic assumptions do not hold water for unique categories, such as Part-103.
Nor should they always be applied in this age of high-tech materials, expanding performance, and ever-changing technology.
IMO... Most aluminum E/AB airplanes designed to only 3.8g, or composite airplane having an ultimate load/limit load factor less than 4; If either is to be built by amateurs, should probably be viewed with some level of skepticism until it is proven in practice with some level of statistical significance.
It seems as if many designers and builders agree, as quite a few popular kits out there are designed to higher than minimum load limits. With this feature being cited somewhat frequently.
This might make a good poll.
