What Are the Physiological Limits of Acceleration in Physics?

[kentyrr]

Greetings!

I have solved too many Physics problems with callous disregard for the practical limitations involved. While a (theoretical) space vessel may be able to accelerate at a rate of 200m/s^2, the human body within probably won't appreciate it very much!

I have trouble constructing practical solutions to many physics-related problems due to a lack of physiological limit information.

For example, what is the maximum "comfortable" and/or "safe" acceleration for a car, train, plane, etc? That question somewhat assumes acceleration in a front-facing, or forward, direction. What about the other directions? What is a similar acceleration limit for a turn, or a deceleration action, assuming that physiological comfort and safety differ according to the orientation of the body with respect to the acceleration vector? Up and down, such as when in an elevator, or perhaps lying prone in a sleeper car on a train...?

I have been able to capture small snippets of limit data from here and there, such as:

• 3g to 4g for brief periods for a well-designed roller coaster ride
• up to 8g for brief periods for fighter pilots (requires a special pressure suit)

I can inspect device specifications to determine limits in use by an industry, but I am seeking information about the limits of endurance, which are not necesarily the actual values employed in our technology today.

I cannot imagine that inexperienced inventors are doomed to a laborious process of (potentially fatal) experimentation with each new idea, nor that they must level-set to such spurious information as seems available.

So, my question is... Are there collections of such physiological limit information? If so, please provide some information as to where such may be located.

Thank you!

Ken

 

[Diffy]

Hello Kentyrr,

I do not know of such a reference that one can simply check. I think that each case needs to be carefully considered in order to establish such limits. For example, what is the maximum (have you considered their might be a minimum?) acceleration that is safe for a car.

This may depend on a number of factors specific to your study. What kind of car, what is the cars weight, how much horse power can the car produce, what environment is the care accelerating in, what are the car's engine specs, etc.

I don't think anywhere there is a standard that a car can accelerate safely at x m/s/s.

The other questions require similar consideration, ie what about the other directions? well what are the cars dimensions, what surface will it most likely be traveling on, etc..

Perhaps you can start with one such physical problem that you are having trouble determining physiological limits for. Then we can start by making assumption about the many questions I have posed back to you, and use mathematical techniques to handle each aspect of the problem step by step.

 

[Danger]

Welcome to PF, Kent.
This seems to be a cross-over post involving both engineering and biology, as opposed to pure physics. Luckily, there are experts in both fields on hand. I'm not one of them.
Nice response, Diffy.

 

[kentyrr]

I'm not sure whether Danger is indicating that this is an inappropriate forum for this discussion. If so, my apologies, and I'd be happy to take it to the correct forum if someone would point the way for me. This definitely combines multiple disciplines, so I rather doubt there is a specific forum that is perfect for this discussion.

My question is posed more from the point-of-view of the vehicle designer, not from the framework of any existing (and already spec'd) vehicle. If I want to move a passenger from point x to point y in time t, what limits much I impose upon my solution, assuming that I can build any mechanism required to accomplish my task. In other words, independent of the particular specifications of any existing vehicle. Once I know the limits, then I can design the mechanism to suit them.

I have two different scenarios that come to mind immediately, although almost any vehicular problem of sufficiently high acceleration would do.

1st scenario, captured from a science-fiction novel: An elevator moves from ground floor to floor 112 in less than 30 seconds. Assumption: each floor is probably 4 m in height, so total distance of movement is 448 m. So I'm reading this, and, assuming we're not using some fictional device such as an "inertial dampener," I wonder if the passengers wouldn't arrive as biological puddles from the acceleration involved, or at least unconscious. This brings to mind the question of what is a "comfortable" acceleration limit to the people within, as well as what might be a "fatal" acceleration limit, if we decide we don't care that they are comfortable.

2nd scenario: Everytime I drive and use my cruise-control, I wonder about how the designers determined the acceleration limits it uses if, for example, I click the "resume" button (which has a previously set target speed of 55 mph) when my vehicle is traveling just 25 mph. Experience tells me that the car does not push the pedal to the metal in its attempt to attain 55 mph in as short a period as possible. Rather, it uses a passenger-accomodating "comfortable" acceleration rate. Which brings to mind a thought that cruise-controls should come with an aggression setting. Wild and crazy teenagers might want speed more than comfort, and select a (slightly) higher acceleration mode, whilst my grand-pappy might want something even lower such that it emulates his particular driving style. So, in the case of the higher acceleration mode, what is the maximum safe acceleration (one would have to account for all those variables you mentioned, including vehicle and payload weight, traction coefficient, surface conditions, acceleration vector in relation to current direction of travel, etc), and, I would assume, even that crazy teenager may not be "comfortable" pushing the envelope to such a safety limit, so (back to creature comforts) what would that "aggressive" limit be (that stays well within safety limits)? This could obviously be determined via experimentation, but surely there is research that helped determine the acceleration limits used in our current cruise-control technology, so one would not need to reinvent the wheel yet again?

I suppose, ultimately, such research may fall under "proprietary information" for each vendor in the industries involved. However, I'd like to think that we have at least some information available on what I would consider COMMON acceleration limits. Human-related data for accelerations in each direction (forward/backward, left/right, up/down), at least. I'm not expecting similar data for Bald Eagles to be available, but humans, yes.

Thank you for your response!

Ken

 

[Danger]

Kent, I definitely was not suggesting that this was the wrong forum. Even if I thought that, which I don't, it wouldn't be my place to say so. That's up to the Mentors. I was merely commenting that it is indeed a multi-disciplinary problem. You'll have to have biologists and/or medical practitioners comment upon the human aspect, and various engineers to evaluate the mechanical side of it.
In the case of the humans, you'll probably have to go with the lowest common denominator; ie: those with physical disabilities. For instance, I used to be a pilot. Now, with the emphysema, anything more than about 1.5g for more than 30 seconds or so could kill me. You'll also have to accommodate diabetics, heart patients, etc., all of whom will have their own individual tolerances.
Sounds like a fun project, but you sure have your work cut out for you.

 

[xzservb]

kentyrr, I am also very interested in the questions you proposed. I'll post what I think, but if you have learned anything else please share.

In what I feel may help:

In introducing acceleration to a human, the greater the (non moving) area that the human is in contact with opposite the acceleration vector, the less pressure they would feel (note: Its easier to accelerate inside a car (your back is agianst the seat), than to stop quickly in an elevator (only your feet are on the ground)).

I personaly would like to accelerate with the front of my body facing the acceleration vector with a surface on my backside in contact with as much of my backside as possible, I feel this would be most comfortable (maybe not the most safe).

This does not address maximum acceleration, only immediate comfort, as I do not know how much pressure the brain can handle agianst the skull, or the heart against a rib, etc.

Therefore in just regarding comfort, the more area opposite the acceleration vector, the better. But in terms of maximum human acceleration and duration, your guess is as good as mine.

When you speak of acceleration limit for a turn, I believe this is no different than just acceleration towards the center of your turning radius (as the only force you feel is opposite the way you turn) and should be considered the same as linear acceleration in terms of physiological limits (you may rotate faster around something, but you'll feel the same as if you accelerating directly towards it). I may be wrong because of the fact that you feel acceleration toward the center even with constant angular velocity (ring world), but I consider a ball on a string, I can make it accelerate rotationaly by only applying force on it towards my hand (the center of rotation). Please correct me if I am wrong about this.

Considering a man in a rocket, I would design a swivel system such that whatever direction the rocket is acceleration, the man would be facing, with his entire backside on something that asorbs pressure well (springs, or foam). If the rocket had jets on both the front and back of the vessel (so it wouldn't have to spin around and waste fuel), the man would face the front during take off, and when the ship slowed down to reach his destination, his body and pressure absorber would turn and face the back. Much like having an office chair on a train, that would spin when you were accelerating/decelerating.

In regards to your elevator problem:

1) You travel 448 meters in 30 seconds.
2) Your average speed is about 15 m/s
3) The way to feel the least force from acceleration is to accelerate half the distance (also half the time) then decelerate the second half.
4) Therefore you would start at 0 velocity, reach a max of 30 m/s (15*2) then end back at 0 velocity.
5) Therefore you need to reach a velocity of 30 m/s in 15 seconds, so (relative) acceleration is 2 m/ss (as is deceleration)
6) Combine that with the effects of gravity, one would experience 7.82 m/ss in the first 15 seconds and 11.80 m/ss in the last 15 seconds. Dividing through by gravity you get .8 g's the first half and 1.2 g's the second half.

Standing up the 1.2 g's may be a little hard on the legs for some people (for me it would be adding 36.5 pounds, from my initial weight of 180 pounds), but I think the majority of people would not mind.

Now that just considers same acceleration and deceleration. If you feel that 1.2 g's should be a maximum, but feel that it would not hurt to go below the .8 g mark, then you can maximize time based off your two different accelerations.

For example if you feel people wouldn't mind .5 g's in the begining, you could cut the time to 25.1 seconds. But the people would only feel the .5 g's for 7.3 seconds, while feeling the 1.2 g's for 17.8 seconds.

If you thought people wouldn't mind free fall in the beginning you could cut time to 23.2 seconds. With the 0 g's lasting 3.9 seconds and the 1.2 lasting 23.2 seconds.

Also you would probably not want to make an instant change from 0 gravity to 1.2 g's, that would be uncomfortable I imagine. I think (peraps) having a bed of springs (like a mattress) between the elevator floor and the floor the people are standing on would absorb some of the initial force and help with the change in acceleration (although the spring stiffness would have to be determined by how much weight was in the elevator at the time).

 

[faitswulff]

On a semi-related note, I was just at 6 Flags Great America pondering similar questions. Anyone here design rollercoasters or know anyone who does?

I don't pretend to have any great understandings of physics, but I was thinking that if you found an equation for acceleration between your chosen velocity (say 15m/s) and v=0 with high orders of contact at the initial and final points of acceleration (where you originally begin to decelerate and when you hit v=0) then it would reduce the jerk at all points.

EDIT - incidentally, that doesn't answer your question of finding what the human limits are. There may be a lot of human factors that vary from person to person, too.

 

[Andy Resnick]

There are safety limits, sure- when designing amusement rides and airbag devices, it's important to take neck support into account. I imagine sports equipment (football pads, motorcycle helments, etc) have the same issues.

http://www.saferparks.org/safety/dynamic_force/research_articles.php
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=233173

There's so many variables involved- points of contact, restraining harness geometry, part of the body (and direction) subjected to a contact force, not to mention the problems in performing the measurements (surprisingly, none of the above studies used cadavers), that the more precise the measurement, the less applicable.

 

[xzservb]

I found this on wiki, it seems to answer most questions posed

http://en.wikipedia.org/wiki/G-force#Human_tolerance_to_g-force