Topic: Terminal Velocity?

[Aotrs Commander]

So, the PCs will be mucking around in an ancient alien terraforming device with a seven-mile deep shaft[1]. It is pretty unlikely any of them will actually fall... But on the off chance... What would be the maximum Fall/Crush attack, do you reckon? (Given that the PCs are in question Liches, the fall won't TECHNIALLY kill them, since Undead regeneration (the terraforming shaft is understandably not on fire), it's not actually a "hand me the character sheet" moment. (Though they might short of their gear!) (Assuming standard gravity and atmospheric resistance.)

Secondly, how many rounds would it take, roughly, do we reckon, in case they try something daring like a rescue in their flying vehicle?



[1]Strictly speaking, at the seven-mile point there's a series of whacking great (offline) turbine blades in a section for another mile and then Giant Replicator Nozzles, but at that fall distance, hitting the fan blades or the replictor nozzles is largely immaterial.

[jdale]

According to https://en.wikipedia.org/wiki/Free_fall

A falling person at low altitude will reach terminal velocity after about 12 seconds, falling some 450 m (1,500 ft) in that time. The person will then maintain this speed without falling any faster.

And https://en.wikipedia.org/wiki/Terminal_velocity

Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 195 km/h (120 mph; 54 m/s).[2] This velocity is the asymptotic limiting value of the velocity, and the forces acting on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.

Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s),[2] which is almost the terminal velocity of the peregrine falcon diving down on its prey.[3] The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to the ground having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study.[4]

Competition speed skydivers fly in a head-down position and can reach speeds of 530 km/h (330 mph; 150 m/s); the current record is held by Felix Baumgartner who jumped from a height of 128,100 feet (39,000 m) and reached 1,357.6 km/h (840 mph; 380 m/s), though he achieved this velocity at high altitude, where extremely thin air presents less drag force.

The biologist J. B. S. Haldane wrote,
    To the mouse and any smaller animal [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object.[5]

The +1/1' fallen formula is linear but the rate of acceleration is not, so it kind of breaks down for extreme falls. I seem to recall +300 being discussed as a cap and it does not seem unreasonable.

At a speed of 120 mph, it will take 3.5 minutes to reach the bottom of a 7 mile pit. That 120 mph speed assumes someone who knows how to fall and is dressed appropriately. You could reasonably say this is the result of a successful acrobatics maneuver, and they have say 3 minutes if the person is falling badly. Either way, there is time for a rescue if the rescue vehicle is fast enough. Of course it starts out flying straight down so there is a nice speed advantage there.

[Aotrs Commander]

According to https://en.wikipedia.org/wiki/Free_fall

A falling person at low altitude will reach terminal velocity after about 12 seconds, falling some 450 m (1,500 ft) in that time. The person will then maintain this speed without falling any faster.

And https://en.wikipedia.org/wiki/Terminal_velocity

Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 195 km/h (120 mph; 54 m/s).[2] This velocity is the asymptotic limiting value of the velocity, and the forces acting on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.

Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s),[2] which is almost the terminal velocity of the peregrine falcon diving down on its prey.[3] The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to the ground having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study.[4]

Competition speed skydivers fly in a head-down position and can reach speeds of 530 km/h (330 mph; 150 m/s); the current record is held by Felix Baumgartner who jumped from a height of 128,100 feet (39,000 m) and reached 1,357.6 km/h (840 mph; 380 m/s), though he achieved this velocity at high altitude, where extremely thin air presents less drag force.

The biologist J. B. S. Haldane wrote,
    To the mouse and any smaller animal [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object.[5]

The +1/1' fallen formula is linear but the rate of acceleration is not, so it kind of breaks down for extreme falls. I seem to recall +300 being discussed as a cap and it does not seem unreasonable.

At a speed of 120 mph, it will take 3.5 minutes to reach the bottom of a 7 mile pit. That 120 mph speed assumes someone who knows how to fall and is dressed appropriately. You could reasonably say this is the result of a successful acrobatics maneuver, and they have say 3 minutes if the person is falling badly. Either way, there is time for a rescue if the rescue vehicle is fast enough. Of course it starts out flying straight down so there is a nice speed advantage there.

Cheers! That'll do fine.

Really should have looked on wiki myself, come to think about it, but I'm rushing a bit... These particular quests (exploration ones) that I write take a lot of writing (the average is currently about 23 pages for a day quest, nearly double something like a more regular RM party or D&D quest!) and I'm running short of time.  I forgot how much effort it takes and didn't start early enough and i'm running out of Mondays - though the advantage of being my own boss means I can at least steal some work-time. So I'm currently just trying to get words on the page and go back and fill-in the little details like this later.

+300 sounds reasonable; it's what you would be at after one round anyway, which was the other possible question and its just theorhertically survivable (if you're a human - as it has happened!). A Lich is likely going smash themselves into the negatives and be out for QUITE some time (especially since I use the breaking 150 rules!) but they will... Eventually... Get up and walkaway from it.

3.5 minutes is plenty good enough estimation, I think (that's 21 rounds, enough time for spellcasting, even!) maybe three if they fumble.

It is an outside possibility that I'll need to anyway, but you never know - RM has gifted us with some quite spectacular spates of collective dice incompetance over the years, so...! (Being so damn thorough is why these quests always take so long to do nowadays...!)

[Jengada]

Not much to add, except for slightly twisted ideas. Since they're liches, how well do you want their bodies to hold up to the winds trying to rip them apart? You could stipulate that once they reach terminal velocity, they take damage at so many points/round from air tearing at them. I mean, it's not going to kill them, as you said, and it will certainly make things more interesting. Plus, it's probably harder to concentrate on preparing a spell when you're coming apart - or even just falling like that, unless you're practiced at it.

[Aotrs Commander]

Wind at termininal velocity doesn't do damage to humans, why would it damage a lich which is significantly tougher?

(Leaving aside the fact they're in full-sealed (transcendant) AT I or VII.)

Actually, technically, they are also, for that matter, only 15% the weight of a human before gear anyway (I had to find an estimate of skeleton weight right before I started this party...!). Which probably means the terminal velocity would be lower and it would take them longer to fall, but the whole +300 cap is good enough fopr a just-in-case scenario.

[jdale]

Actually, technically, they are also, for that matter, only 15% the weight of a human before gear anyway (I had to find an estimate of skeleton weight right before I started this party...!). Which probably means the terminal velocity would be lower and it would take them longer to fall, but the whole +300 cap is good enough fopr a just-in-case scenario.

Storywise, it probably doesn't matter, but for the sake of being pedantic, it actually makes a big difference if they weigh less and have the same surface area, since terminal velocity is determined by the balance of the force of gravity (based on weight) vs air resistance (based on area and velocity). According to https://www.omnicalculator.com/physics/free-fall-air-resistance it's a difference of 58.2 m/s (130 mph) for a human vs 22.6 m/s (55 mph) for a lich (assuming a weight of 185 lbs/83 kg for the human and 12.5 kg for the lich). That means the lich's terminal velocity is equivalent to the velocity a human would reach after just 28 meters (92 feet). That would be a +92 fall attack. There's some variability in the numbers based on which site you are looking at but you could round it to +100.

Also, if the terminal velocity is only 55 mph, it will take 7.6 minutes to hit the bottom, which is more time to find a solution.

[Nightblade42]

Side note from the guy trolling this thread: I love how realistic we can get with RM (as this thread demonstrates).  Hence the old buy line (which I Truly miss):

Get Real, Get Rolemaster!

 

[Aotrs Commander]

Actually, technically, they are also, for that matter, only 15% the weight of a human before gear anyway (I had to find an estimate of skeleton weight right before I started this party...!). Which probably means the terminal velocity would be lower and it would take them longer to fall, but the whole +300 cap is good enough fopr a just-in-case scenario.

Storywise, it probably doesn't matter, but for the sake of being pedantic, it actually makes a big difference if they weigh less and have the same surface area, since terminal velocity is determined by the balance of the force of gravity (based on weight) vs air resistance (based on area and velocity). According to https://www.omnicalculator.com/physics/free-fall-air-resistance it's a difference of 58.2 m/s (130 mph) for a human vs 22.6 m/s (55 mph) for a lich (assuming a weight of 185 lbs/83 kg for the human and 12.5 kg for the lich). That means the lich's terminal velocity is equivalent to the velocity a human would reach after just 28 meters (92 feet). That would be a +92 fall attack. There's some variability in the numbers based on which site you are looking at but you could round it to +100.

Also, if the terminal velocity is only 55 mph, it will take 7.6 minutes to hit the bottom, which is more time to find a solution.

Oh. Okay. wow. I... Had not considered it would make that much of a difference.

Heck, it's at the point I may have to do an approximation tking equipment into account! (The Liches get their carrying capacity as if they were alive - partly because otherwise it would be ridiculous - and (the fighter-types anyway) are in full combat gear, so that's actually... *checks*

Okay, adding in the weight or their armour and assault packs and combat armour webbing (which is treated as "worn" and not towards their carrying limit[1]), they are carrying between 25 to 35kg, and the total weight range runs between about 37kg to about 55kg - so yeah, the equipment weight is actually more significant than the body weight!

Playing with the numbers on the afore-linked site, looks like at that, it's between about 500m to 700m (for the 37 and 55 ends) to reach terminal velocity (i just plugged fall distances in until the maximum was the same as the terminal!), so... Actually, how did you get the 28m for the 12.5 kg? Fiddling with the height suggests - with the air resistance, which might not have been accounted for - that it's be 170m before reaching terminal velocity. Did you equate the +300 to human terminal velocity and reduce proportionally or something?

(That's a fracking useful calculator you linked, I'll be filing that away. (Hell, I can even modify the gravity to whatever (close-but-not-quite 1g) I set it too...!))

[

Side note from the guy trolling this thread: I love how realistic we can get with RM (as this thread demonstrates).  Hence the old buy line (which I Truly miss):

Get Real, Get Rolemaster!

 

The great irony, I always find, is that despite that, thanks to our friends the open-ended rolls, I've seen more ridiculous things come out in Rolemaster than any other system...!



[1]Which is 1 or 5kg respectively (their armour is slightly more advanced than regular kinetic armour), 4kg and 1 kg, so another 6-11 kg on top of their little-bit-under 20kg to little-bit-over 30kg dead-weight loads.

[jdale]

Playing with the numbers on the afore-linked site, looks like at that, it's between about 500m to 700m (for the 37 and 55 ends) to reach terminal velocity (i just plugged fall distances in until the maximum was the same as the terminal!), so... Actually, how did you get the 28m for the 12.5 kg? Fiddling with the height suggests - with the air resistance, which might not have been accounted for - that it's be 170m before reaching terminal velocity. Did you equate the +300 to human terminal velocity and reduce proportionally or something?

I used the calculator backwards. Enter the weight for a human, then start reducing the altitude distance until the Max Velocity equals the terminal velocity I calculated for a lich.

[Aotrs Commander]

I used the calculator backwards. Enter the weight for a human, then start reducing the altitude distance until the Max Velocity equals the terminal velocity I calculated for a lich.

Oh. That's what I did but I had to get it to 170m (still at the +300 range) before it matched with 12.5kg.

Wait, hang on... Simpliest explanation:  *checks* Yeah. 28m works for 2.5kg; I hazard maybe you did it twice (because the 22.6m/s for 12.5kg was the right velocity) and made a typo on the mass the second time?

[jdale]

No, 83 kg, altitude of 28m, gravitational acceleration of 9.807, air resistance of 0.24 kg/m, results in time of fall 2.4 sec with a maximum velocity of 22.5 m/s. Note that it still says terminal velocity of 58.2 m/s but in this 28m fall for 2.4 sec, that's not reached.

Maybe you are adjusting the altitude while leaving the mass at 12.5? If we are looking for the equivalent fall for a human, that would be the human mass of 83 kg.

[Nightblade42]

[

Side note from the guy trolling this thread: I love how realistic we can get with RM (as this thread demonstrates).  Hence the old buy line (which I Truly miss):

Get Real, Get Rolemaster!

 

The great irony, I always find, is that despite that, thanks to our friends the open-ended rolls, I've seen more ridiculous things come out in Rolemaster than any other system...!

That's very true.   

[brole]

Hey all.
I was flicking through companion V and found an 'official rule'.
Gravity Law spell list p. 36. notes terminal velocity and rates of fall.

Seems like the companions have a rule for everything.

[Aotrs Commander]

Ha! Should have figured there would be one somewhere, but that's sort of an obscure place for it to be. Not something I would have found myself, save for chance!

Having said that, that same spell list's Fly spell giving you the 15'/rnd = 1 mph is something I've always remembered as a useful approximation, so...!


By-the-by, as it happened, my PCs were not hapless enough to fall into the pit and sensibly stayed inside their flying APC; but you can garentee if I hadn't thought about it, they would have done. As dear old Sam Gamgee oh so very wisely said "if you haven't got it, you shall want it...."

[Cory Magel]

Hence the old buy line (which I Truly miss):
Get Real, Get Rolemaster!
 

I've still go the T-Shirt.