Whats the relationship between efficiency and speed?

[Matabele]

Ive just checked out some reviews done by Blacky Schwarz and get the following figures:

Bow Model            Efficiency           Speed
Black Swan Hybrid   86.5%      191fps
ACS CX         84.3%      192fps
Predator Custom recurve   82.8%      193fps

So Im confused, why does the Black Swan have the lowest speed but have the highest efficiency, and the opposite is true for the Predator? Wouldn’t the most efficient limb, pass that energy on and also produce the highest velocity? And why the disparity between efficiency and velocity values, i.e. the speed ratings are all within 1-2fps of each other but the efficiency values span almost 5%?

Has it got to do with the peak weights being different, even though the gr/lb values have been standardized at 9gr/lb for the tests?

Just curious as to how to get the most from the information.

[Molson]

The bow weights were a little different.

[hunt it]

Buy a Morrison and you'll have alot of both!  

[Jeremy]

Efficiency is a calculation based on a calculation made from multiple measurements      Each measurement has an error associated with it (both from the sensitivity of the scale and measuring method)  You can make mulitple individual measurements to help with that, but there's still the error and that needs to be taken into account, especially when doing down stream calculations.  The % efficiency really should be given as +/- the error.  My guess, it's at least +/- 2%.

The speed is a measurement.  Still has an error associated with it, but it's at least not compounded by making multiple calculations.

[Thueb]

From what I know of bow efficiency, it is calculated by dividing kinetic energy by the bow wt.  So the relationship between speed and efficiency is the way speed effects KE.  Now before I go any further, this simplified because if you’re a physics guru you get all worked up about Newtons, Jouels, SI measurements, weight isn’t weight its mass, and the like.  Its all irrelevant for this short blurb of bow efficiency.  

I’ll try to stay out of the math weeds, but KE is ½ mass times velocity squared. So the more speed a bow will produce with a given arrow wt, the larger the numerator of the efficiency calculation (if all other variables remain the same).  Larger numerators equal more efficiency.  However, if you increase bow wt, without increasing arrow velocity, the denominator of the efficiency calculation increases.  Larger denominators equal less efficient bows (again assuming all other variables stay the same).  

Of course more bow weight usually equals more speed, so this is really a ratio of (arrow wt and arrow speed)/ bow wt.  

I hope that helps.  Here is a web url that gets into the math weeds.   http://granjow.net/projects/bow/BowEfficiency.pdf

[Thueb]

I forgot to add, obtaining 100% bow efficiency is impossible because of vibrations, arrow paradox, air resistance on the bowstring and a list of other factors that rob energy.  I would say anything over about 80% efficient is truly top of the line…  I calculated out the efficiency of my Bob Lee at around 70%, but that was with slow heavy arrows.

[Jeremy]

Efficiency is calculated by dividing the kinetic energy by the stored (potential) energy.  The stored energy is calculated from the f/d curves (area under the curve).

The most efficient bows aren't necessarily the fastest     It just means that particular bow design is good at transferring the energy it does store to the arrow.

[Dartwick]

The efficiency number he uses is not of practical significance to the shooter.

If you care about performance only 2  energy related numbers that matter.

-how much it stacks arourd your draw length(less stack is easier to shoot and control.)

-the arrow velocity(or KE)(when the arrow mass to draw weight ration is constant across bows being compared).

[Matabele]

Great info here, thanks for posting! I'll have to mull this over for it to sink in, but basically if Ive got it right the speed rating is the figure to watch for, all else being equal.

[Jeff Strubberg]

Think of it this way.

Efficiency is how much you get out of what you got.

Speed is how much you get.

200fps out of a 70 pound bow is fast.  200fps out of a 50 pound bow is efficient.

[Thueb]

Matabele,

When it comes to speed the answer is, yes and no.  Speed will make an efficient bow, but usually you have to give up arrow weight to do it.  My 64lb Bob Lee could smoke out light arrows, but I’m decreasing arrow mass to do it; KE has a mass component.  Both speed and arrow mass play a part.  Short of playing with some arrows of different weights and a chronograph, I couldn’t tell you exactly how the relationship works.    

If it were me, I wouldn’t worry too much about efficiency ratings, especially if there were only 3-5% difference.  Many other things come into play that are far more important, most of which are subjective, like the bow’s shootability.  I’d take a forgiving inefficient bow that shoots where I look any day over an efficient critical one.  Besides that, all your modern bows will be plenty efficient for hunting.  But if you’re into setting flight records, that is something else entirely.

Jeremy is right efficiency is calculated by using the potential energy, or the area under the force draw curve, but that is too cumbersome to work with and makes me have flashbacks of Calculus.  If you do a dimensional analysis of KE/bow wt the units don’t cancel out to give a true efficiency.  But for a quick down and dirty comparison between two bows, KE/bow wt. works.  He’s also right that there is a +or- error of a couple of percent.

[Thueb]

I like the way Jeff said that "200fps out of a 70 pound bow is fast. 200fps out of a 50 pound bow is efficient."

[O.L. Adcock]

Draw weights have nothing to do with it, both of those bow could/should be the same efficiency.

It's simply a ratio of what you put in compared to what is put out. 2 - 50# bows will not necessarily store the same energy. If I know the se/pdf of the bow and efficiency, I know how fast it will shoot. If I only know efficiency, I have no idea how fast it will shoot. Seeing a bow that shoots as fast or faster then another that has a lower efficiency rating, that means it stores more energy then the other is all. The final number is the only thing that matters in the end.

Thueb, "I calculated out the efficiency of my Bob Lee at around 70%, but that was with slow heavy arrows."  

You might want to take a closer look at how bows work. They all get more efficient as arrow weight go up. If you got the opposite, you made an error somewhere...O.L.

[Guru]

Jeff, How could it be that simple? You can make any bow, be it 50# or 70#, shoot 200fps.

Are you talking the same weight arrow?

[Carbon Caster]

Originally posted by Jeff Strubberg:
Think of it this way.

200fps out of a 70 pound bow is fast.  200fps out of a 50 pound bow is efficient.

IF you are using the same arrows out of each bow that could be a correct statement.  Otherwise it is meaningless.  Weight and speed are not linear.  a 70 pound bow and a 50 pound bow of the same design "should" shoot a 700 and a 500 grain arrow respectively at the same speed.

[L82HUNT]

Originally posted by Matabele:


Bow Model            Efficiency           Speed
Black Swan Hybrid   86.5%      191fps
ACS CX         84.3%      192fps
Predator Custom recurve   82.8%      193fps

[/QB]

All I know is I ordered one of these bows yesterday.  And was told with my 26" draw and a 600 grain arrow I would see 190fps+.

[Molson]

I see what you are saying OL and it's confusing in that a bow can store more energy, but be less efficient. Comparing a BW PL against a Predator recurve, both have an 82.8% efficiency  and both are 50.5 lbs, yet the Predator shoots about 10 feet faster.  If a bow with a lower or same efficiency can store more energy and shoot a faster arrow, then what qualities does the effiency rating show the bowhunter? Would it be more indicative of other things like handshock and noise?

[O.L. Adcock]

Molson, "then what qualities does the effiency rating show the bowhunter? "

Really nothing by itself. It could be an indication of noise/vibration, an 80% efficient bow compared to a 75% that stores 43ft/lbs compared to an 80% that stores 40...Both will shoot the same speed but the 80% bow will have 28% less wasted energy to make noise and vibration with....O.L.

[Guru]

Originally posted by L82HUNT:
 

Originally posted by Matabele:


Bow Model            Efficiency           Speed
Black Swan Hybrid   86.5%      191fps
ACS CX         84.3%      192fps
Predator Custom recurve   82.8%      193fps

[/b]

All I know is I ordered one of these bows yesterday.  And was told with my 26" draw and a 600 grain arrow I would see 190fps+. [/QB]

Unless you're going to shoot 80#'s, I doubt very seriously that you can get a 600gr. arrows out of a bow 190fps at your 26" draw.....

[L82HUNT]

Originally posted by Guru:
[/ [/QB]

Unless you're going to shoot 80#'s, I doubt very seriously that you can get a 600gr. arrows out of a bow 190fps at your 26" draw..... [/QB][/QUOTE]

Thought the same thing, not that bowyers add numbers up are anything.  We shall see in a few months, when she comes.  The bow weight is mid 60's