Trad Talk Forums banner
1 - 20 of 21 Posts

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #1 ·
My apology might be for possible misleading information. which could be seen as over egging one pudding to under egg another.

Webster posted that interpolating the inch by inch measurements gives a different value to the sum of the inch by inch values taken for a dfc.

My mission of being online has been to show people that its not that hard to measure bows, and in doing so have tried my best to keep it simple.

Now. I cant vouch for what ever method other folks use to work this out.
but here goes.

three measurements taken for simplicity sake.
First inch
6lbs
second inch
9lbs
Third inch
11lbs


Simple Sum of this would give:
11+9+6 = 26 inch pounds of energy.

Interpolate this into half inch values.
first half inch
3lbs (half of six)
First inch
6lbs
First inch and half
7.5lbs (average of 6 and 9)
Second inch
9lbs
Second inch and half
10lbs
third inch
11lbs

total stored energy
3+6+7.5+9+10+11
46.5 half inch pounds. so divided by 2 to give inch pounds
23.25 inch pounds.


as you can see sub dividing means you end up with a different answer to using whole values.

but as a means to keeping it simple using the whole inch is just as valid for comparison to comparison.

trouble arises when you compare the two methods.
and that is where im guilty and for that I apologise. I haven't stopped to think of the differences.


That said. It over eggs the Stored energy
so that delivers a under estimated Efficiency.

and for some reason this didn't occur to me, So here I am owning up to my own focus not letting me see some potholes in arguments.


a DFC is a DFC, but how you arrive at the area under it is where the debate can start I suppose.

as I have openly stated our methodologies have been publically posted so open to criticism all the way along.
 

·
Premium Member
Joined
·
12,452 Posts
Calculus is like that. You don't understand your error until you miss Mars a few degrees. :).

I have a masters in math that has been little used since the 80s. These discussion have me breaking out my calculus books. Actually I have missed math.
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #3 ·
Calculus is like that. You don't understand your error until you miss Mars a few degrees. :).

I have a masters in math that has been little used since the 80s. These discussion have me breaking out my calculus books. Actually I have missed math.
all methods are valid. as long as they are consistant. My error has been assuming Blacky and other bow testers, have used the simple method. when it looks like they havent.

I took some of blackies numbers and compaired them to ours. and it looks like the stored energy calculations are not the same.
so this arrives at different Stored energy, which leads to different efficiency numbers
 

·
Premium Member
Joined
·
3,004 Posts
Sid,

There are programs that calculate the space between the 1 inch numbers and solve for the area under the curve. Otherwise you end up with a DFC that has a stair step instead of a smooth line. John uses one that was developed by Norb years ago that does it all.

I've even plotted the DFC on our design system and have it connect the dots and solve for the area. It actually works very well.

The idea is to get the actual and accurate stored energy to work with otherwise all other measurements are not accurate.

Mike
 

·
Registered
Joined
·
1,505 Posts
Sid,

Totally agree that the most important thing is to use a consistent form of measurements for comparative purposes.
The most accurate is really only important when defining absolute (non caomparative) measurements.

That is the reason I asked you and Mat, earlier on, how you both calculated stored enegy.

Found out it was being done somewhat differenty. LOL
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #7 ·
Yeah, Mike. thanks... I have crossed two concepts. both are right!
crossed over they are not.

The sum of the inch is fine. It works well. its just it delivers a different answer to other methods.
its still compariable. to other numbers derived from the same method.

I have been trying to keep life simple for those that don't want to get too deep into things. kinda like a homeBrew kit to looking at bows.

What I haven't done is explain that there are differences between home brew and more official techneques.

I think I will stick to the home brew techneques. as they allow people to do the simple maths.

our computer bow model accounts for limb mass and limb mass COG, as well as the Mass of the string. Bows and modeling them, can get as mad on maths as you want. Most folks accuse me of being too technical, so an "abraviated" method is just as good.
as long as its understood.

same as GPP actually doesn't work as bow performance benchmarks. 90lbs bows don't quite perform like 30lbs bows. but the assumption is that it does.

does it make a difference between a 45lbs bow and a 50. Not really. but does it matter between a 90 and a 30. yes it does.
so Gpp is regarded as ok to use. so can measuring stored energy for comparative reasons as long as both are done using the same method...

and for that im here "fessing up" to my mistake
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #8 ·
I suppose its exactly like measuring AMO draw length or draw length to the throat of the grip.

both are right for the intended purpose. both are accurate. are they comparable. NO.
 

·
Civil but Disobedient
Joined
·
10,696 Posts
Sid,

I often use the linear DFC approximation for formulas that I derive to explain certain properties of bows. It is similar to what you are talking about here. Differences are the key. You can do a lot with approximation methods. My research adviser just won the Nobel Prize doing that. The problem is when folks use the approximations incorrectly, or inappropriately. Approximate methods will often produce decent differences, even if they miss the absolute numbers. A discussion of differences leads directly to why I focus my testing on comparisons, and set up my program to do comparisons, rather than focusing on absolute numbers. Absolute numbers with nothing to compare them to are not that meaningful.
 

·
Registered
Joined
·
465 Posts
There is a simple trick to get a more accurate answer that would be consistent with linear interpolation between points. Simply add 1/2 of the last measurement instead of the full value. This will make the two methods give the exact same answer, and the answer will also be closer to the true integrated energy.

With the given example, we would get ...

Method 1: E=11/2+9+6 = 20.5 inch pounds of energy.

Method 2: E=(3+6+7.5+9+10+11/2)/2=20.5 in-lbs

This method will always give exactly the same answer because linear interpolation draws a line between the points and the method gives the area assuming lines are drawn between the points (it's called the trapezoidal rule).
 

·
Civil but Disobedient
Joined
·
10,696 Posts
SteveB,

Yes the trapezoidal rule is very good for well behaved functions like DFC's. That is the approach that I use. I have verified the results for my calculations using smaller trapezoid widths. I don't think there is a need to do anything more complicated.
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #15 ·
Longbowguy:
The covert hunter is the first bow we have went and published stored energy numbers.

Normally its just been a % gain over a last model

But if ive made a mistake. Ill do my best to make it clear where i have and how to get the truth by helping to see its consiquences

If its a comparison of our data to our data. The results are valid. If its our data to someone elses. Then yes. Its invalid.
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #16 ·
Hank. StevenB

Whats to stop the subdevisions happening again. For example finding the difference between two points gives one answer.
Sub deviding that again into 1/4s gives a different answer again.
Which is why our internal work has been based on the full inch, just to bypass this issue.
 

·
Registered
Joined
·
5,581 Posts
Discussion Starter · #17 ·
10
20

Can be seen as
5
10
15
20

Or it can be seen as
2.5
5
7.5
10
12.5
15
17.5
20
All these come to different stored energy values

What about 1/8ths.
If you see my point.
 

·
Registered
Joined
·
465 Posts
10
20

Can be seen as
5
10
15
20

Or it can be seen as
2.5
5
7.5
10
12.5
15
17.5
20
All these come to different stored energy values

What about 1/8ths.
If you see my point.
Let's do them using the trapezoidal rule.

20 becomes (20/2)*2=20, assuming a 2 inch step from 0 to 20

Can be seen as

10
20 which becomes (10 +20/2)=20 (this is the 1 inch step)

Can be seen as
5
10
15
20 which becomes (5+10+15+20/2)/2=20 (step becomes 1/2 here)

Or it can be seen as
2.5
5
7.5
10
12.5
15
17.5
20 which becomes (2.5 + 5 +7.5 + 10 + 12.5 + 15 +17.5 +20/2)/4=20
 

·
Registered
Joined
·
465 Posts
We actually talked about this in another thread, although I can't remember which one. I mentioned that the error of the other method (I call it the step rule) gets smaller for a real bow measurement. These examples give bigger error. In my view the error is probably smaller than the typical measurement error anyway. So the step rule is not unreasonable to use. I think my point ( and Hank would agree I think) is that the modification to the math for the trapezoidal rule is so easy (just cut the last measurement in half before you add it) that we might as well do it. Also, the fact that this method is consistent with linear interpolation, which is what most people do, is another benefit.
 

·
Registered
Joined
·
1,505 Posts
Steven,

As I stated previously, that is the method I used to calulate the stored energy feom Blackie's review.

Nice thing is, it's easy to set up on a spread sheet, like this.

DL DW SE
9 0
10 5 2.5
11 8 6.5
12 12 10
13 14 13
14 17 15.5
15 18 17.5
16 21 19.5
17 22.5 21.75
18 25 23.75
19 27 26
20 28.5 27.75
21 30.5 29.5
22 32.5 31.5
23 34.7 33.6
24 37 35.85
25 39 38
26 41.5 40.25
27 44 42.75
28 46.5 45.25

Total in/ilbs SE 480.45
Total ft/lbs SE 40.0375
 
1 - 20 of 21 Posts
This is an older thread, you may not receive a response, and could be reviving an old thread. Please consider creating a new thread.
Top