Jump to content

Archived

This topic is now archived and is closed to further replies.

VARIABLE

Velocity vs. Distance

Recommended Posts

...

You information allowed me to compare my mental notes of gun performance and put it all into some sort of context that reduced some of the variables that were confusing the issue.

....

Thanks, Blazer. Very nice feedback. On some of the other forums I read posts where people are trying to calculate such things... hopefully this information will help them (or answer their questions).

 

---------------------------

 

VARIABLE, just a a few questions to clarify. The graphs are part experimental and part calculated?  Shouldn't it first be testing experimentally and then try to fit a model over it?

The first post explains which parts are experimental and which are calculated. For ranges beyond 60', it became difficult to record readings. The calculations themselves have been verified for trajectory with no hop-up. So of the five figures listed (listed as figs 6, 8 , 10, 12, & 14), figure 8, concerning hop-up, is the only one that needs more experimenting before I’d feel comfortable saying that it’s an accurate depiction of projectile trajectory. The tweaks will not affect the other graphs at all -- I consider those to be finalized.

 

As for which comes first, experimentation or a model… well, it’s part of the scientific process. Any physicist will first try to drum up all of the equations necessary to predict what they’re looking for. Then they do testing to see how close they were, and finally tweaking on the model to make it match the observations. It’s important to make calculations first otherwise you might find yourself with a bunch of data and no mathematical way to express it. For the most part, the observations match the model almost perfectly, with very few tweaks.

 

Aside from the governing equations drag, and kinematics, how did you account for hop up?  Thats something I am unsure on how to model.  I know that we can take a lifting body as an assumption on how the BB acts, and its velocity is directly associated with the lift it has.

The article on Lift (force) that’s on the Wikipedia is as good as any place to start. They even take the equation down to an algebraic expression for you. It explains far better than ever could on this forum.

http://en.wikipedia.org/wiki/Lift_force

 

You can also calculate the Magnus Force for lift, however this method is only useful if you’re dealing with fairly static lift coefficients and the equation is something of an over-simplification. Magnus lift could be calculated in a fairly precise manner but the standard lift equation is easiest to use. Magnus lift is calculated slightly differently but the overall calculation is the same. If you’d like to read about it, here’s a link to an article written by Dr. John Carini at Indiana University:

http://carini.physics.indiana.edu/E105/spinning-balls.html

 

It also points to an article by Dr. Leroy Alaways that’s both interesting and helpful for calculations.

 

The coefficient of lift is a tough variable to calculate. It changes constantly with relation to spin velocity and linear velocity. Furthermore, spin velocity isn’t a static variable, either. Instead, it’s constantly decreasing. One of the hold up’s in my work is that the calculations I’m coming up with wherein I calculate torque and the exponential spin decay don’t seem right. Once I’m able to perform additional tests, I should be able

 

Seriously, look at the wiki article and let me know if that helps you or not. I’d be happy to answer any questions or offer suggestions, feel free to PM me.

 

---------------------------

 

Tell me, you write that you chronoed the BBs at distances up to 60', have I read that correctly?

 

How do you chrono' a BB in flight when more than a few feet from the gun or am I missing something here?

I thought chrono's were extremely sensitive to alignment and even when placed at the barrel/muzzle end were prone to false readings and light interference.

Shooting through the gates at 60’ is much harder than shooting through them at point blank range, but it can be done. People do it all the time. In fact, when I chronograph actual firearms, per the instructions that come with these units I set the chronograph 10-15 feet away from the barrel for safety considerations. I’m not sure what the source of your consternation comes from on this. Maybe I’m missing something; I could be reading your question wrong.

 

Alignment is important, but it wasn’t an issue for the tests (meaning that we visually checked for proper alignment). As for false readings and light interference, light interference can be an issue but good testing conditions minimize this. When you say “false readings” I’m not sure what you mean, specifically. To me, it means measurements where one shot does not get recorded by either the first or second gate. The two chronographs that I use give an error reading if only one of the photogates registers a shot. At range, the readings were consistent with a small standard deviation. Some shots didn’t go through the photogates at some of the longer ranges but for the most part it worked well. The key to collecting good data is good setup.

 

Let me know what it is concerning the chronograph measurements that seems odd... I'll try to respond as best as possible.

Share this post


Link to post
Share on other sites

VARIABLE,thanks for the articles, will read up on them soon.

 

Since this was one of the things I wanted to model as well, I was met with difficulties in the same way when conducting the experiments as well as trying to work out the lift on the BBs. I would've gone down the path of doing an empirical curve fitted model rather than a functional model because lift is difficult to calculate.

Share this post


Link to post
Share on other sites
Shooting through the gates at 60’ is much harder than shooting through them at point blank range, but it can be done.  People do it all the time.  In fact, when I chronograph actual firearms, per the instructions that come with these units I set the chronograph 10-15 feet away from the barrel for safety considerations.

In my experience the best chrono's for distant shots are the ones with 2 wide gates. With these, the key issue seems to be to have a bright, even, light source on them. I'm sure shafts of sunlight through a window, when you're indoors, can mess them up but I've found that accuracy degrades much more often when you have poor light or cloudy weather.

In fact, I've seen several chrono companies selling "lighting kits" as well, which usually consist of a silver umbrella and a powerful UV emitting bulb.

 

Also, FWIW, you should always place a chrono a good distance from the muzzle when shooting real-steel (unless the chrono specifically demands otherwise) cos you often get tiny fragments of powder or bullet shooting out with the bullet which might, theoretically, cause dodgy readings.

Share this post


Link to post
Share on other sites
Hop-up doesn't add a great deal to range cos it imparts lift by causing the BB to spin backwards. This in turn, reduces the forward velocity of the BB.

 

A BB fired without hop-up (off a high place) would travel further although it would drop as it flew.

Another BB fired with hop-up would travel a flatter trajectory but actually come to a stop sooner.

 

In the real world, of course, hop-up is usefull cos you're only ever going to be, at most, a couple of metres above the target so ultimate range isn't ever an issue. It's getting the longest possible distance which is still accurate that's important.

 

I see wht you mean now.. So you mean the max possible range is decreased when hop is added (ie the range you get if you fire a AEG in a artillery cannon style). But agreeing with wht I said, effective range increases when hopup is added..which is basically the range you get if both AEG with hop and without hop are fired at close to horizontal at a low height above ground.

Share this post


Link to post
Share on other sites

First off - Great info! I have been in airsoft hibernation for a while and this is pulling me back in rather quickly.

 

http://carini.physics.indiana.edu/E105/spinning-balls.html

 

It also points to an article by Dr. Leroy Alaways that’s both interesting and helpful for calculations. 

 

 

 

I was wondering when Dr. Alaways' name was going to come up. He has been put into the Baseball hall of fame (so he told us) for mapping points on a baseball during the flight of a thrown curve ball.

 

I had a few classes under him at the California Maritime Academy (for Mech. Engineering). Weird guy, terrible professor. He got booted around the same time we noticed he was living in one of the empty labs.

 

 

He used a MatLab program to map the points. I wonder if there was a way to getc and use, this program for what you are trying to do Variable? If he can do it for a curve ball, there has got to be a way to do it with a bb.

 

(edited for spelling)

Share this post


Link to post
Share on other sites
First off - Great info!  I have been in airsoft hibernation for a while and this is pulling me back in rather quickly.

....

Terrible professor?! That's a shame, he seems to have a keen interest in relating physics to sport. Of course if I had a nickel for every physicist who turned out to be a lousy instructor...

 

MATLAB is very handy -- I used it immensely for a lot of the analysis I did in my previous job. And... I've used it some to verify the results I'm getting. In comparing the work that I calculated to that of others, we found some discrepencies in extreme cases. After spending a lot of time questioning our equations, we found that it was small errors in computing methods used that led to greater errors down the line. Some of the folks have used straight algebraic techniques for the calcuations, others have used software to integrate and differentiate, that latter of which is what I did. Matlab would certainly make plotting the data easier than the current method (simply because of it's ability to automate such tasks) but the end results have been the same, which is fine for me.

 

I did verify the results using MATLAB and using different methods (high-iteration algebraic, medium-iteration Euler-method, and low-iteration Runge-Kutta method). Each method delivered the same results, though Runge-Kutta wasn't advantageous simply because all of the points needed to be plotted.

 

Unfortunately, I lost my copy of MATLAB during Hurricane Katrina along with the LINUX box I was running it on. If I get a replacement copy or just repurchase it, I'll probably try to compile a program for people do download... but this would be well down the line. In the mean time, I'll have to use other methods for plotting all of the data.

 

By the way, when I was working as a researcher I spent about two solid years of my life living at sea either on MSC ships or US Navy vessels and worked with a few guys from CSU-Maritime -- nice foilks / good school.

 

...I would've gone down the path of doing an empirical curve fitted model rather than a functional model because lift is difficult to calculate.

I think that an empirical curve would be helpful if a lot of the information needed weren't already out there, or if the calculations were insanely difficult. Of course, we are lacking in some of the data which is why I'm having to do some testing now. Lift really isn't the issue inasmuch as calculating spin decay is. I still think that it's helpful to have as much insight going into this problem as possible.

 

As I've found, taking data is tedious and time consuming, my worry in empirically analysis is that it would be necessary to test a multitude of BB masses, a mutlitude of ranges, a multitude of muzzle energies, etc. As it stands now, I'm only looking to see what results I get in the tests and see if they deviate wildly from the current calculations. If they're good for a small sample of different weights, different masses, and different muzzle energies, I'll publish the results with confidence.

Share this post


Link to post
Share on other sites

Well I'd be the last one to reccomend MATLAB over software like Excel (I am much better with the latter).

 

It is funny that you mention the 'assume' problem with MATLAB, I have heard of something similar in the past. I was just a student back then. A place where if everyone gets the same results, it doesn't matter what reality is - the group answer becomes reality.

 

CMA grads as a whole are pretty good (for never learning much, if any, design engineering or analysis). Boy can we turn a wrench though.

 

A while back I took some data based on barrel lengths vs springs vs hop up settings. I'll see if any of it pertains to what you have been working on.

Share this post


Link to post
Share on other sites
A is area in square meters (I took the average size of a bb to be 5.95mm, so the area should be 0.0000278051 m^2 (and area is calculated as A = pi * radius ^2)

 

Your formula there is correct but you should do surface area of a sphere, not a circle. The 5.95 mm (.00595m) i believe is the diameter of the sphere which makes the radius close to about 3mm (.003m).

 

The formula for the surface area of a sphere is:

 

4πr^2

 

Thus, making it:

 

4π(.00009)

 

.000036π

 

Assuming π is around 3.14159,

SA≈.00011309724

 

I highly doubt it will change the information very much but sorry if this actually is blasphemy but i am pretty sure this is correct.

Share this post


Link to post
Share on other sites
Your formula there is correct but you should do surface area of a sphere, not a circle.

Basically, you're asking the question "When calculating drag, should you calculate the area for a sphere or for a circle?"

 

Using the area of a sphere as opposed to that of a circle would cause the calcuations to be quite different. However, when calculating simple drag we're only concerned with the cross-sectional area of the object. In this case, the cross-section of a sphere is a circle, which is why the area calculated is for that of a circle. If this doesn't quite make sense, let me know and I'll try to explain it using some intuitive examples...

Share this post


Link to post
Share on other sites
:/ Drag should actually be half the surface area of the sphere.. since its only half which is receiving friction.. You should just double the area of the circle then.

 

If you’re unsure of the effects of drag, you might consider posing your posts as a question rather than a statement, as making an overt statement can be misleading to some…

 

Calculating drag here is the same as if you were calculating the drag of an airplane moving through air or a submarine moving underwater. We’re primarily concerned with two components of parasitic drag, major emphasis being placed on “profile drag” (sometimes referred to as “form drag”) and minor emphasis placed on “interference drag” (which is mainly used for calculating drag when the object is spinning, i.e., hop-up is applied). To state it outright, drag deals primarily with displacing the medium that it is passing through, rather than the friction generated due to object-medium interaction.

 

Profile drag ONLY deals with the object’s profile. This is the two-dimensional shape an object makes when looked at head-on with respect to the direction it is traveling. If you look at a sphere head-on, it appears as a circle. The area calculated for this would be the area of a circle. It's as simple as that...

 

We’re not overly worried about friction drag with an object such as this because, at these speeds, friction drag makes a relatively negligible contribution to the overall force of drag. Even so, if air is moving past any part of the object, then that part is experiencing friction drag. Which is to say that friction drag is calculated over the entire sphere, and not just one half. But that’s a different equation and, again, it is so negligible that it’s not even worth calculating.

 

We are, however, concerned with interference drag. This is caused by the turbulent airflow creating shed wake after the BB has passed. This component causes the drag coefficient to change from roughly 0.39 to 0.65. Even so, a Cd of 0.39 is achieved momentarily when the ratio of spin to forward velocity reaches a critical threshold, and Cd > 0.50 is achieved only for high-spin/low-velocity situations. The mean Cd will be around 0.46 or 0.47. Dr. Rabi Mehta has published a paper that deals with the drag variance due to an object’s radial velocity and is the best source for determing the drag coefficient relative to the ratio of rotational velocity to linear velocity.

 

I’m not sure where you got the idea that you’d need to calculate area over three dimensions for determining drag… but to do so is incorrect. No worries… if you have any questions about this, please feel free to ask away.

 

Cheers,

Variable

Share this post


Link to post
Share on other sites

Yeah that's exactly why I love this sport. There's a lot going on when launching these 6mm's. I enjoy tuning them as much as shooting people with them.

Share this post


Link to post
Share on other sites

Wow, I never thought of it that way. This whole time I had always assumed that the fact that a .20 BB traveling at a faster initial rate would mean that it would go further. If your facts are percise (which I am convinced they are) then a .25 BB would also have a distinct advantage in the wind to right?

Share this post


Link to post
Share on other sites

As a newbie to airsoft and as a long time air rifle engineer I have been hugely impressed by the hard work and maths, thanks to all .

I now use .28s in my 'warm' VSR-10 BUT I always use .23s in my AEGs as my non mathematical method of testing was to get 2-3000 each of .20, .23 and .25 and see which 'behaved the best out my guns. .23s are not so common in the airsoft shops in the UK, I get mine from airsoft jockland.

The same argument has raged on for about 10 years in the airgun world, basically whether .177 (4.55mm) .20 (5mm) and .22 (5.5/5.55mm) is better at delivering killing force (8ft/lbs+) at up to 30meters and the maths supported .20cal, both for retaining energy and having a flatter trajectory, as accuracy is particularly important. We do not want to wound wildlife, we want a humane kill.

(My Genesis for example, delivers +/- 2 fps, sending a 14.4 grain out at 612/613 fps all day long.)

Nonetheless, the majority of airgun manufacturers of both spring and precharged airguns still produce and sell vastly more .22s!! Expect this to run and run and run...

Share this post


Link to post
Share on other sites

Per someone's request, I'm adding the link to the article which is a work-in-progress (the original post became buried).

 

The friction coefficient used for hop-up calculations is a little off -- I'll modify it as I get better information. In the interim, here's the link:

The Airsoft Trajectory Project

 

If anyone has any questions about the physics of airsoft, send me an email and I'll try to offer some insight.

 

Cheers,

VARIABLE

Share this post


Link to post
Share on other sites
I wonder what the results of a Tanio Koba Twist barrel would be?

It does not affect muzzle velocity or backspin of the BB. It's supposed to keep the BB off the walls of the barrel by creating an air vortex with the rifling. Whether it works to help accuracy or not, I don't know. But it doesn't make the BB fly further, given that the velocity, weight and backspin are the same. It's just impossible.

 

-Sale

Share this post


Link to post
Share on other sites

×

Important Information

By using this site, you agree to our Terms of Use and the use of session cookies.