The principle of dimishing returns as it applies to bow building

[hedgeapple]

Most things reach a point where adding something to them does not increase their effectiveness as much as it did.  Here's my 2 scenarios and questions.

Premise:  The wood for each bow is equall.  The tillering is spot on.  The mass theory applies to each.  We're making these bows from the same hickory tree.  They are all pyramid style.

1. The bows are 66" ntn, all drawing 28". So, we make a different bow in 5 pound weight increments starting at 40# and going to 70# or more.  Let's use fps as a measuring tool.  At some point does the draw weight reduce the speed?

2. Second variable: We're making a 50# from our 66" ntn stave, then reducing and/or adding 2" to the ntn length.  At  what point we lose any benefits from the length, shorter or longer?

[PEARL DRUMS]

Tim Baker already did all that for you Dave. Paul Comstock did lots of similar testing. You can find that info in his pamphlet.

[hedgeapple]

Thanks Pearly, I assumed someone had don't this research.  I'd just never seen any conversations about it here.  Per chance could you directed to this info, that is if you have it close at hand.  Otherwise, I'll do a web search.

[PEARL DRUMS]

Sure. Chapter three in the trad bowyers bible one. And in Paul Comstocks "The Bent Stick"  section 8, page 10-12. Good stuff in both.

[steve b.]

1.  No

2.  If you are saying the 50# stays the same at all lengths then, yes, longer bow has more wood so more sluggish eventually.  Shorter bow would eventually stack.
  If you are saying the 50# would vary according to the changes made then the shorter bow would draw heavier and be faster.  The longer bow would pull lighter and have the mass problem too.

[RyanY]

As PD said we already have a good understanding of these things and the info had been publishers with regards to the second question, longer bows can be made with the same limbs as shorter bows with an extra long handle section so moving mass is the same. Speed diminishes after a certain length due to string mass eating up efficiency, not sluggish limbs. This is discussed in TBBV1 in the design and performance chapter.

[Del the cat]

1. At some point the wood fails.
2. At some point the long one becomes heavy and sluggish. The short one starts to stack and/or the wood fails.
There is a relatively small window of bow dimensions for any particular wood. Say for a 28" draw at 50# using Yew, it would be unwise to go shorter than 56" or longer than 80". But in practical terms, you wouldn't want to go more than say 2" taller than the archer or shorter than say 60".

IMO.
The real diminishing returns comes with increasing draw weight, you get to a point where you don't gain much arrow speed, but you gain power E.G you can throw a heavier arrow.
Del

[Jodocus]

While I was of the firm opinion that lenght will per se be a negative factor, That a bow should be only as long as necessary, Baker, in TTBB4, states that longer bows will always cast better than shorter ones (p. 173, t leat in my german edition).
I don't know if this is true, can't tell from my limited experience.

I still make mine rather short. 

[George Tsoukalas]

Increasing draw weight does not reduce speed. Mass at the tips does unless kept constant. Short bows stack unless recurved so that would limit functionality.

I always design the bow around the wood and the projected draw weight I want. My bows are hunting bows.  The arrow is away silently.

Look at the physics of it. Use the formula rate x time = distance. Time =distance/ rate. Let's use 60 ft. as our distance and 100 + the bow's weight as the measure of a decent bow shooting a 500 grain arrow.  Out of a 50 # bow the arrow arrives in 0.4 sec. Out of a 70# bow the arrow arrives in 0.35 sec. Everyone, can draw their own conclusions.
Good discussion.
Jawge

[Sidewinder]

I love reading you brainiacs discussing these types of topics. I've learned alot in the past. Don't usually have a lot to say but I'm watching none the less.   Danny

[Slackbunny]

Are you familiar with the idea of the flight envelop for airplanes? If not, the flight envelop is basically just a graph that shows all the possible speeds that a plane can possibly fly at all of the altitudes that a plane can possibly fly. Its made up of two curves that define the abilities of the aircraft at different speeds and altitudes. A plane can never fly out of its envelop (unless it goes into a dangerous dive). Each type of plane has its own unique flight envelop.

There is a similar principle with bows, but the variables would change to things like bow length and width, Aspect Ratio, bow weight, and arrow speed. While the flight envelop can be represented fully in 2-D, I think you would need a 3-D graph or contour graph to fully plot the performance of a specific bow design. The peak of the surface would be the peak arrow speed and would define the conditions required to reach it. Something like this would be an interesting project, but its practicality would be limited given the great variation of wood quality even with the same species.

[Carson (CMB)]

Like Del pointed out, heavier bows provide more power by casting a heavier arrow. 

I used Stu Miller's Dynamic Spine Calculator (a great tool for determining required arrow spine from your bow's specs) to calculate the energy of an arrow from two different scenarios:

50# bow shoots a 500 grn arrow 177 fps = 34.9 ft-lbs
70# bow shoots a 700 grn arrow 177 fps = 48.8 ft-lbs

A difference of 13.9 ft-lbs or 40% difference.   That is a big difference, and one that matters when hunting certain big-game species.  The diminished return mentioned in TBB by Baker regarding draw weight is that the heavier the bow the harder to shoot accurately.  It might be practical to point out that heavier bows are more difficult to shoot, but from a pure performance perspective, I think that discussion is a distraction.  It takes lots of training to shoot heavy bows accurately but there is a big pay-off in terms of arrow energy and penetration power.

[hedgeapple]

Thanks to everyone who has posted.  I appreciate it.  Now I need to buys some books.