Common Calculation Concerns: Skull Crushing and FTE Movement

[KatBoi69]

Back on skull crushing...I'm not a materials engineer, but I found the following articles that may be of some use if anyone with more skill in structural engineering can chime in.

Why are your bones not made of steel? - Materials Today

Read ‘Why are your bones not made of steel?’ on Materials Today – the gateway for mechanical properties news.

www.materialstoday.com

Ultimate Strength of the Human Femur – Body Physics: Motion to Metabolism

openoregon.pressbooks.pub

The Mechanical Properties of Bone | O&P Virtual Library

www.oandplibrary.com

 

[KLOL506]

Back on skull crushing...I'm not a materials engineer, but I found the following articles that may be of some use if anyone with more skill in structural engineering can chime in.

Why are your bones not made of steel? - Materials Today

Read ‘Why are your bones not made of steel?’ on Materials Today – the gateway for mechanical properties news.

www.materialstoday.com

Ultimate Strength of the Human Femur – Body Physics: Motion to Metabolism

openoregon.pressbooks.pub

The Mechanical Properties of Bone | O&P Virtual Library

www.oandplibrary.com

Pretty sure the femur and the skull have different yields for surviving compression. In the second article it says the femur can withstand 6000 lbs of compressive force.

Guess it looks like the 1100 lbs value and the 6.5 GPa value from the Washingtonpost article is our best bet.

 

[KatBoi69]

Pretty sure the femur and the skull have different yields for surviving compression. In the second article it says the femur can withstand 6000 lbs of compressive force.

I guess what I've gleaned from that article is, after the femur, the temple is the next strongest bone in the body (oddly) and stress only depends on the area a force is applied over.

Given that info, I'm tempted to say "bone is bone" and use 6000lbs, but also, given that your skull isn't all temple bone and the temple is second to the femur, 1100 lbs sounds like a decent ballpark to smush a human skull.

Either way, 1100 lbs sounds very reasonable, given 6000 lbs as the upper limit of any bone.

 

[KLOL506]

I guess what I've gleaned from that article is, after the femur, the temple is the next strongest bone in the body (oddly) and stress only depends on the area a force is applied over.

Given that info, I'm tempted to say "bone is bone" and use 6000lbs, but also, given that your skull isn't all temple bone and the temple is second to the femur, 1100 lbs sounds like a decent ballpark to smush a human skull.

Either way, 1100 lbs sounds very reasonable, given 6000 lbs as the upper limit of any bone.

EDIT: Nah, prolly wouldn't work, it'd need PSI values. (I am talking about some other method BTW, not about this quote.)

We'd need to find some way to be able to convert this into energy.

 

[KatBoi69]

EDIT: Nah, prolly wouldn't work, it'd need PSI values. (I am talking about some other method BTW, not about this quote.)

We'd need to find some way to be able to convert this into energy.

What'd the OG version of this say? Lol.

Hm. HM. That needs what, a timeframe?

 

[KLOL506]

What'd the OG version of this say? Lol.

Hm. HM. That needs what, a timeframe?

OG version of what I initially thought was just false. Eventually I remembered this would require the force to travel over a certain distance.

The average human head is 22 cm tall, 0.22 meters. 1100 lbs is 4893.044 newtons.

4893.044 newtons over a distance of 0.22 meters is 1076.46968 J (Street level) which is way too ******* low for a skull (Considering even full power punches from boxers and MMA fighters can't do much damage to a skull and even fast and brutal kneecaps only slightly dent in the skull), also I was told somewhere that energy derived like this is apparently not the right way to calculate energy for applying force in this manner (Could be wrong tho, initially this was for pulling something up and not crushing something downwards). Plus, the 6.5 GPa statement in the Washingtonpost article which I found recently.

 

[KatBoi69]

OG version of what I initially thought was just false. Eventually I remembered this would require the force to travel over a certain distance.

Classical mechanics, my least favorite part of physics.

I want to say you could imply a distance from the art through some common sense and pixel scaling. I'd imagine you wouldn't need to push much past the thickness of the skull itself before the damage becomes catastrophic/qualifies as crushing.

 

[Antvasima]

Thank you for helping out DontTalk. So what do you think that we should do here?

@DontTalkDT

 

[KLOL506]

Classical mechanics, my least favorite part of physics.

I want to say you could imply a distance from the art through some common sense and pixel scaling. I'd imagine you wouldn't need to push much past the thickness of the skull itself before the damage becomes catastrophic/qualifies as crushing.

So I shifted to the next method.

Converting the psi value (psi to pascal)

Then dividing the pascal value with surface area in meters squared

Then I multiplied the result with the value of the skull's height itself (0.216-0.2 meters tall on average).

The 6.5 GPa value goes into 9-A territory (42 megajoules, 2x baseline 9-A, absurdly too high), but the 1100 lbs goes into 49 kJ territory.

Problem is, the 1100 lbs value is in force, it's not explicitly mentioned as pressure. So I'm not too comfortable in assuming it as a PSI value.

 

[KatBoi69]

So I shifted to the next method.

Converting the psi value (psi to pascal)

Then dividing the pascal value with surface area in meters squared

Then I multiplied the result with the value of the skull's height itself (0.216-0.2 meters tall on average).

The 6.5 GPa value goes into 9-A territory (42 megajoules, 2x baseline 9-A, absurdly too high), but the 1100 lbs goes into 49 kJ territory.

Problem is, the 1100 lbs value is in force, it's not explicitly mentioned as pressure. So I'm not too comfortable in assuming it as a PSI value.

Can you type the math? I think I see an error BUT it might be a typo

Edit: OK, so the error was a typo. Is the 1100 pound figure from one of the published studies? In that case, they may have the size of the piston applying the force in the supporting information.

 

[KLOL506]

Can you type the math? I think I see an error BUT it might just be due to phrasing.

Sure.

OK, so assuming skull height is 22 cm or 0.22 meters based on average human head height (Sources are wikipedia and this). This is our travel distance.

From this article, I see the skull being 15cm wide and 20cm long (0.15 and 0.2 meters respectively, wikipedia also gives similar numbers), so the area is 0.03 meters square, let's use this as our area upon which the force is applied.

==1100 lbs force end==
1100 psi is 7584233 pascals or newton per meter square.

7584233 pascals over an area of 0.03 m^2 is 227526.99 newtons.

Work is force times distance, the distance travelled is 0.22 meters so: 227526.99*0.22= 50055.9378 joules (Wall level)

Again, the 1100 lbs value is in force, not in PSI.

==6.5 GPa end==
It's already in GPa so we can just convert it to Pa

6.5 gigapascals is 6500000000 pascal or 6.5e+9 pascal.

6.5e+9 pascal over an area of 0.03 m^2 is 195,000,000 newtons.

195000000 times 0.22 meters (Since 0.22 meters is the height of the skull and also the downwards distance travelled) is 42,900,000 J (Small Building level)

 

[DontTalkDT]

@DontTalkDT

I haven't been following on the skull crushing debate, so I can't say anything about that.

I don't know if we need to do something regarding FTE feats. I believe we have just been ranking them as subsonic up to now, which we would still do for most reasonable feats. I guess we need to keep in mind that the lighting should be reasonable, that camouflage like things shouldn't happen and that the distance shouldn't be too huge for them in the future.
I suppose I could write a note about that somewhere... just not sure where.

Guess I can write a basic note on the Speed calc section of the calculation page.

 

[KatBoi69]

I haven't been following on the skull crushing debate, so I can't say anything about that.

I don't know if we need to do something regarding FTE feats. I believe we have just been ranking them as subsonic up to now, which we would still do for most reasonable feats. I guess we need to keep in mind that the lighting should be reasonable, that camouflage like things shouldn't happen and that the distance shouldn't be too huge for them in the future.
I suppose I could write a note about that somewhere... just not sure where.

Guess I can write a basic note on the Speed calc section of the calculation page.

Maybe we can devise a short checklist someone can go down to see if their FTE feat qualifies as subsonic? Could literally be a "Is this FTE Legit?" Checklist page with a few questions the reader needs to ask themselves and the reasoning behind it.

Skullcrushing argument is just "****, uh, why are there no good numbers for this?" We might be approaching qn answer but I think the onus is on me to skim one of the papers to find the area of a piston involved (but I'm visiting family rn and will try to find that later).

 

[DontTalkDT]

Maybe we can devise a short checklist someone can go down to see if their FTE feat qualifies as subsonic? Could literally be a "Is this FTE Legit?" Checklist page with a few questions the reader needs to ask themselves and the reasoning behind it.

Well, something like that. Are there more criteria than the three I mentioned? If it's just the three I might just keep it in the form of one or two short sentences. Probably no need to make a proper checklist for three criteria.

 

[KatBoi69]

Well, something like that. Are there more criteria than the three I mentioned? If it's just the three I might just keep it in the form of one or two short sentences. Probably no need to make a proper checklist for three criteria.

I'll review the thread. I know that I've seen some people give very long lists of qualms with FTE feats meaning anything before (usually as a rhetorical device tbh).

 

[KatBoi69]

Sure.

OK, so assuming skull height is 22 cm or 0.22 meters based on average human head height (Sources are wikipedia and this. This is our travel distance.

From this article, I see the skull being 15cm wide and 20cm long (0.15 and 0.2 meters respectively), so the area is 0.03 meters square, let's use this as our area upon which the force is applied.

==1100 lbs force end==
1100 psi is 7584233 pascals or newton per meter square.

7584233 pascals over an area of 0.03 m^2 is 227526.99 newtons.

Work is force times distance, the distance travelled is 0.22 meters so: 227526.99*0.22= 50055.9378 joules (Wall level)

Again, the 1100 lbs value is in force, not in PSI.

==6.5 GPa end==
It's already in GPa so we can just convert it to Pa

6.5 gigapascals is 6500000000 pascal or 6.5e+9 pascal.

6.5e+9 pascal over an area of 0.03 m^2 is 195,000,000 newtons.

195000000 times 0.22 meters (Since 0.22 meters is the height of the skull and also the downwards distance travelled) is 42,900,000 J (Small Building level)

We're a bit screwed on this, even though the math looks good, that paper has no dimensions on the piston used to exert the force.

 

[KLOL506]

We're a bit screwed on this, even though the math looks good, that paper has no dimensions on the piston used to exert the force.

Yeah so I just went with assuming the area of the top of the skull as an estimate, which I assumed to be 0.03 m^2 based on head width being 0.15 meters and head length being 0.2 meters).

 

[KatBoi69]

Well, something like that. Are there more criteria than the three I mentioned? If it's just the three I might just keep it in the form of one or two short sentences. Probably no need to make a proper checklist for three criteria.

Here's my thought on FTE:
1). I think the issue that hasn't been addressed here is the "implied observer" of the thing moving FTE. We usually aren't looking through the eyes of a character, so imo, there needs to be a standard assumption about who we consider the "observer" for an FTE feat or some evidence needs to be given. This could just be the main combatant the mover is being tracked by imo unless something implies otherwise.

2). The next question is, what is the observer's skill level? What is the fastest thing we know they can see of comparable size in the series. whoever is moving FTE to that viewer should scale above the speed of that fastest observed thing (if available).

3). If we don't have an estimate for what they can see, we can assess their skill level and use 13ms (for no clear training) and 5ms (for someone with obvious combat skill) per the articles posted up thread by Jason.

4). Include a list a factors that may make the feat bs. DT mentioned all relevant ones that I can find: good lighting, no camo, reasonable size/distance of object (edit: oh, and obviously if the observer is literally stated to have bad eyesight, missing glasses, etc).We could even look up that air-force study if it's available to get some irl bounds on what those terms mean. This article was useful if anyone wants to review it (https://www.cambridgeincolour.com/tutorials/cameras-vs-human-eye.htm#resolution)

I feel like I'm overcomplicating this, but those are all of the factors I can imagine.

Yeah so I just went with assuming the area of the top of the skull as an estimate, which I assumed to be 0.03 m^2 based on head width being 0.15 meters and head length being 0.2 meters).

If you're comfortable with that, I am. I'll look at the math more closely since it could end up being a final calc.

 

[DontTalkDT]

Here's my thought on FTE:
1). I think the issue that hasn't been addressed here is the "implied observer" of the thing moving FTE. We usually aren't looking through the eyes of a character, so imo, there needs to be a standard assumption about who we consider the "observer" for an FTE feat or some evidence needs to be given. This could just be the main combatant the mover is being tracked by imo unless something implies otherwise.

2). The next question is, what is the observer's skill level? What is the fastest thing we know they can see of comparable size in the series. whoever is moving FTE to that viewer should scale above the speed of that fastest observed thing (if available).

3). If we don't have an estimate for what they can see, we can assess their skill level and use 13ms (for no clear training) and 5ms (for someone with obvious combat skill) per the articles posted up thread by Jason.

4). Include a list a factors that may make the feat bs. DT mentioned all relevant ones that I can find: good lighting, no camo, reasonable size/distance of object (edit: oh, and obviously if the observer is literally stated to have bad eyesight, missing glasses, etc).We could even look up that air-force study if it's available to get some irl bounds on what those terms mean. This article was useful if anyone wants to review it (https://www.cambridgeincolour.com/tutorials/cameras-vs-human-eye.htm#resolution)

I feel like I'm overcomplicating this, but those are all of the factors I can imagine.

1) Actually, I would assume it's normal human vision unless implied otherwise. We usually don't get to see with character's super senses and stuff.
2) I feel like that is a different issue. That's basically just that blitzing a character scales above its reactions in speed. Don't think that needs to be clarified beyond what the Reactions page already does.
3) I mean, as I said in my reply to Jasonsith's post (and as was the subject of this thread), it's not as simple as taking timeframes. Heck, if you have a fan turn it on and there is a good chance the edges of the fan blades seem to disappear. And that despite the fact that they are the whole time in your field of view.
4) I suppose "does not have bad eyesight" could be added, even if quite obvious.

 

[KatBoi69]

1) Actually, I would assume it's normal human vision unless implied otherwise. We usually don't get to see with character's super senses and stuff.
2) I feel like that is a different issue. That's basically just that blitzing a character scales above its reactions in speed. Don't think that needs to be clarified beyond what the Reactions page already does.
3) I mean, as I said in my reply to Jasonsith's post (and as was the subject of this thread), it's not as simple as taking timeframes. Heck, if you have a fan turn it on and there is a good chance the edges of the fan blades seem to disappear. And that despite the fact that they are the whole time in your field of view.
4) I suppose "does not have bad eyesight" could be added, even if quite obvious.

1). That's a hard sell in concert with how movement calc is treated. If some characters are calc'd at ftl+, obviously the viewer is given some kind of "buff" to perceive that. We aren't seeing with normal human senses when we observe these characters in a series (if you believe the calcs). Also a lot of FTE feats are accompanied by the other combatant, or an observer going "I can't see that". It's probably something that needs to be taken into account, as arguments will otherwise go "well it isn't just you who can't see, character x who can see character y move at speed z can't see it."

2). Ability to react to and ability to see are two very different things. I can see a car about to hit me and be unable to react to it in a meaningful way.

3). Yes, that's why there is a list of four points.

4). Yeah it's the only other thing I could think of, but eh, you want to be complete.

Overall I really can't tell where you stand on this issue. Summarize your position?

 

[Antvasima]

I haven't been following on the skull crushing debate, so I can't say anything about that.

I don't know if we need to do something regarding FTE feats. I believe we have just been ranking them as subsonic up to now, which we would still do for most reasonable feats. I guess we need to keep in mind that the lighting should be reasonable, that camouflage like things shouldn't happen and that the distance shouldn't be too huge for them in the future.
I suppose I could write a note about that somewhere... just not sure where.

Guess I can write a basic note on the Speed calc section of the calculation page.

That seems fine to me. Thank you for helping out.

 

[KatBoi69]

I think I'll leave the idea of implied observer to a separate CRT.

 

[DontTalkDT]

1). That's a hard sell in concert with how movement calc is treated. If some characters are calc'd at ftl+, obviously the viewer is given some kind of "buff" to perceive that. We aren't seeing with normal human senses when we observe these characters in a series (if you believe the calcs). Also a lot of FTE feats are accompanied by the other combatant, or an observer going "I can't see that". It's probably something that needs to be taken into account, as arguments will otherwise go "well it isn't just you who can't see, character x who can see character y move at speed z can't see it."

2). Ability to react to and ability to see are two very different things. I can see a car about to hit me and be unable to react to it in a meaningful way.

3). Yes, that's why there is a list of four points.

4). Yeah it's the only other thing I could think of, but eh, you want to be complete.

Overall I really can't tell where you stand on this issue. Summarize your position?

1) Many calcs do result in us seeing super fast... however, those calcs have proof for that. Furthermore, we also often don't see super fast if you look at how often characters seem to disappear even if they don't do so for the character in question. Take, say, Saitama fights against Speed of Sound Sonic or something. That fact that we usually don't share the special perception of the Sharingan or other super sense techniques further shows how we rarely share the actual perception of the character.
If we know a character sees nothing we can always use that character's vision.
It's not really all that relevant, though. Unless the character has less than human vision we just end up in the same case as human vision speed wise because
2) What you are suggesting would be scaling from perception time, I think, which we don't do. Trying to calc with the perception of characters would result in calc stacking at that. In any case, I think such scaling considerations are an issue for the reactions page instead.
3) Yeah, but even if those 4 points are given it doesn't justify using 13ms or anything like that. That's my point. FTE can get Subsonic under those conditions, but you still can't do any kind of simple calc with some timeframe.

 

[KatBoi69]

1) Many calcs do result in us seeing super fast... however, those calcs have proof for that. Furthermore, we also often don't see super fast if you look at how often characters seem to disappear even if they don't do so for the character in question. Take, say, Saitama fights against Speed of Sound Sonic or something. That fact that we usually don't share the special perception of the Sharingan or other super sense techniques further shows how we rarely share the actual perception of the character.
If we know a character sees nothing we can always use that character's vision.
It's not really all that relevant, though. Unless the character has less than human vision we just end up in the same case as human vision speed wise because
2) What you are suggesting would be scaling from perception time, I think, which we don't do. Trying to calc with the perception of characters would result in calc stacking at that. In any case, I think such scaling considerations are an issue for the reactions page instead.
3) Yeah, but even if those 4 points are given it doesn't justify using 13ms or anything like that. That's my point. FTE can get Subsonic under those conditions, but you still can't do any kind of simple calc with some timeframe.

Point 1: Hm, I think maybe I'm trying too hard to preempt arguments that will come up down the line. You're pointing out the kind of nuance I'm thinking of addressing. All I was really proposing with this was leaving a note on that list about these nuances. If it's being overly thorough, no need to spend the time on it.

Point 2: I'd only be suggesting scaling, no calcs, because given the variability in what can be FTE irl, it makes sense to allow some flexibility beyond assigning one value to FTE.

Point 3: Again, I don't want to add any actual calculation into this. My impression was that the idea that FTE is subsonic came from that article about fighterpilots having 5ms reaction time, and again, wanting to offer flexibility, I thought it might be useful to have a way to put some chars into normal human perception timeframe of 13ms.

Overall, most of our disagreements seem to be related to me thinking a bit too much about the implications of these changes and maybe some miscommunication. At the end of the day, the things I'm proposing here could be tabled for a different thread while you just make the notes you see are reasonable.

 

[Antvasima]

I don't know if we need to do something regarding FTE feats. I believe we have just been ranking them as subsonic up to now, which we would still do for most reasonable feats. I guess we need to keep in mind that the lighting should be reasonable, that camouflage like things shouldn't happen and that the distance shouldn't be too huge for them in the future.
I suppose I could write a note about that somewhere... just not sure where.

Guess I can write a basic note on the Speed calc section of the calculation page.

So about this...

 

[DontTalkDT]

Point 2: I'd only be suggesting scaling, no calcs, because given the variability in what can be FTE irl, it makes sense to allow some flexibility beyond assigning one value to FTE.

You can't get speed from a reaction time without a calc, though.

Point 3: Again, I don't want to add any actual calculation into this. My impression was that the idea that FTE is subsonic came from that article about fighterpilots having 5ms reaction time, and again, wanting to offer flexibility, I thought it might be useful to have a way to put some chars into normal human perception timeframe of 13ms.

Subsonic FTE comes form the fact that we can see people moving at subsonic speed, such as skydivers and motorcyclists, meaning that FTE characters need to be faster than those. For the time being the 5/13 ms figures aren't used.

So about this...

Calculations

In order to determine a character's Destructive Capacity, we must first look through the character's feats, and determine how much energy was exerted to preform such a feat. Sometimes the destructive capacity of the feat can be determined easily with no need of a calculation, but most of the...

vsbattles.fandom.com

I added something. Hope everyone is ok with that until someone finds a better solution.

 

[KLOL506]

You can't get speed from a reaction time without a calc, though.


Subsonic FTE comes form the fact that we can see people moving at subsonic speed, such as skydivers and motorcyclists, meaning that FTE characters need to be faster than those. For the time being the 5/13 ms figures aren't used.

Calculations

In order to determine a character's Destructive Capacity, we must first look through the character's feats, and determine how much energy was exerted to preform such a feat. Sometimes the destructive capacity of the feat can be determined easily with no need of a calculation, but most of the...

vsbattles.fandom.com

I added something. Hope everyone is ok with that until someone finds a better solution.

I'm fine with this.

 

[KatBoi69]

You can't get speed from a reaction time without a calc.

This bit was just about using fte relative to the same observer to ballpark the speed of the thing moving fte. I don't really care about reaction time related to this point. I was just highlighting that FTE movement could be scaled instead of being given a set speed under certain circumstances.

The parts related to reaction times were a separate thing that was apparently less relevant to the current basis of why FTE is subsonic than I realized.

Edit: also, the addition looks satisfactory to me.

 

[Antvasima]

The note looks good to me as well, but should it not be added at the bottom of the Speed page instead, or maybe to both?

 

[Ugarik]

FTE can still be calculated. I will explain you how it works. It's not that complicated

 

[Ugarik]

The concept of FTE movement is simple. A human eye and rotate at a speed of 700 degrees per second or 12.2 rad/s. If the angular speed of a moving object relative to your eyes is above 12.2 rad/s the object goes blur.

The difficult part is determening the linear speed of an object using its angular speed and position requires calculus.

 

[Antvasima]

Thank you for helping out Ugarik.

I haven't seen you in a while. I hope that you are doing okay.

 

[Antvasima]

The note looks good to me as well, but should it not be added at the bottom of the Speed page instead, or maybe to both?

@DontTalkDT

So about this...

 

[KatBoi69]

The concept of FTE movement is simple. A human eye and rotate at a speed of 700 degrees per second or 12.2 rad/s. If the angular speed of a moving object relative to your eyes is above 12.2 rad/s the object goes blur.

The difficult part is determening the linear speed of an object using its angular speed and position requires calculus.

That's really clever. My concerns are that I'm not sure how many feat scenes will have the data to do the calc, and you might run into "well, they aren't human, maybe their eyes move faster" arguments.

Either way, that's a way more clear description than any of the articles we've read.

 

[Ugarik]

Basically, this is how you solve these kinds of problems. The problem is that you need to know the location of the moving object

 

[KatBoi69]

Basically, this is how you solve these kinds of problems. The problem is that you need to know the location of the moving object

Oh that's actually not too hard, because you'd just end up using the answer to that calculus as a generalizeable formula. You may still run into issues on the "well, do we really know their eye only moves at human speed" end, but hey, nice to know it's doable.

 

[Ugarik]

Well in the most simple case, the speed to go blur would be just "distance from the object times 12.2"

let's say the object 5 m from your face goes blur. The speed should be at least 12.2*5 = 61 m/s. And this is the low-end formula so I think it can be used pretty much everywhere.

 

[KatBoi69]

Well in the most simple case, the speed to go blur would be just "distance from the object times 12.2"

So if the object is let's say 5 m from your face and it goes blur. It's speed should be at least 12.2*5 = 61 m/s. And this is the low-end formula so I think it can be used pretty much everywhere.

Hmm. My gut says we need to test this to see if we can recapitulate the answers from one of the FTE studies listed in this thread to make sure this formula isn't too abstracted from physical reality.

 

[DontTalkDT]

The note looks good to me as well, but should it not be added at the bottom of the Speed page instead, or maybe to both?

I think the note on the calculation page suffices.

The concept of FTE movement is simple. A human eye and rotate at a speed of 700 degrees per second or 12.2 rad/s. If the angular speed of a moving object relative to your eyes is above 12.2 rad/s the object goes blur.

The difficult part is determening the linear speed of an object using its angular speed and position requires calculus.

I believe that neglects relevant factors as I mentioned in detail here:

To comment on this:

One factor that is neglected here is the way the eye averages things out, which is a major factor. Take a camera flash for example. Those can easily be in the range of about 1/300th or 1/1000th of a second, yet you would never miss them. One reason for that might be that it is seriously blinding, but another is the relative amount of light. So much light of the camera flash enters the eyes, and activates the receptors, that the rest of the surrounding light doesn't fall as much into weight, even if it enters for a longer timeframe. The brain just favours the strong input and neglects the weak.
Now, bright flashes are not that much an issue but think about colour contrast. At the point where things get hard to see dark green on light green background would likely faster blur/vanish than dark red on a light blue background. The difference in the input is simply higher.
Of course brightness hence also has a role in that, not just for bright flashes. That is further complicated, as our eyes are better at detecting differences in (relatively) dark scenes than they are in bright scenes. That's for example also why computers usually assign more colours to the dark end of the spectrum, than to the light one.

With that things already get very complicated. And then comes the little circle you mentioned, the fovea centralis, which sees only the central 2° of the visual field. It sounds easy to say we should consider just that, but our vision is actually created by focusing on several area's in rapid succession with the best part and our eye then doing magic calculations to put that together in the image we see.

That link in general does a good job of showcasing of how our eye might work like a camera, but our vision has a ton of post-processing of our brain applied. That's exactly why we have stuff like optical illusions. And that's basically what we are talking about here, the optical illusion of something being blurry or even invisible.

Hence I'm not quite comfortable with putting together a formula for FTE stuff outside of simple comparisons (like motorcyclists or skydivers). Saying anything that isn't camouflaged will be seen if it's within the 2° of our best vision for more than 1/30s of a second is making the calculation without considering our brain's influence. That's the part I don't think we can overcome unless we find actual scientific research that just has a formula in it.

Unless you know of a study that approves of that method of course.

 

[Antvasima]

I think the note on the calculation page suffices.

Well, the problem is that most of our members and visitors do not really visit the calculation instructions pages, whereas they do visit the speed page. So I think that it might be a good idea to add it as a footnote there.