Primitive Archer

Main Discussion Area => Bows => Topic started by: Kegan on March 11, 2011, 02:57:05 am

Title: WHY are short bows slower?
Post by: Kegan on March 11, 2011, 02:57:05 am
Trying to sort this out while my short irons are still in the fire:

Say there are two well designed bows, one 66" the other 56". The 66" is straight and the 56" is reflexed enough to have a similiar F-D curve. However, it seems that even with less mass and no stack the short bows don't shoot faster. I can only guess that their less mass is cancelled out by the less leverage, correct? Is that the trade off or am I missing something else?

Thanks in advance, hopefully the next set of sticks I finish will be able to shed some light as well :)
Title: Re: WHY are short bows slower?
Post by: fishfinder401 on March 11, 2011, 03:09:30 am
mabey you removed some of the weight in the wrong place, cancelling out the weight reduction, some of my fastest bows are short
hope this helps a little
noel
Title: Re: WHY are short bows slower?
Post by: Del the cat on March 11, 2011, 04:54:54 am
I dissagree with your assertion.
However for any particular style of bow and wood there must be an optimum length, longer or shorter than that would reduce the performance.
If you take a set of carbon limbs from a modern target bow (spits on floor) and mount them in risers of widely differing lengths you will change the performance...but we then get into the realms of geometry beyond my furry cat brain.
Del
Title: Re: WHY are short bows slower?
Post by: medicinewheel on March 11, 2011, 05:05:05 am
...
If you take a set of carbon limbs from a modern target bow (spits on floor) ...

Funny
Title: Re: WHY are short bows slower?
Post by: Shaun on March 11, 2011, 11:35:43 am
It is my unscientific observation that shorter bows are faster. 

or am I missing something else?  ...distance traveled by the limb mass (where the mass is on the limb), length of working limb, modules of elasticity of the limb material, etc. 

also... faster can be relative to arrow mass/draw weight ratio, ie. flight bows vs hunting bows.

Title: Re: WHY are short bows slower?
Post by: NTD on March 11, 2011, 01:48:29 pm
"One of the cruel realities of bow design is that shorter straight bows can't be as fast per pound as longer straight bows even at equal draw length.  Bewteen 35" and 60" possible performance rises roughly 1 fps per inch of bow length.  Cast rises slowly from there to around 68" then only minor improvement from there to 80" and only then if given a more elliptical tiller."

-Tim Baker
Traditional Bowyer's Bible IV
Title: Re: WHY are short bows slower?
Post by: NTD on March 11, 2011, 01:50:42 pm
So that supports Kegans assertion, Del, Fish, and Shaun, Now let's get back to WHY.
Title: Re: WHY are short bows slower?
Post by: sharpend60 on March 11, 2011, 03:39:30 pm
I always thought of it like a power stroke.
Thus making longer draws and longer bows faster.

The Bowyers Bible 4 seems to support that.

On the other hand, shorter bows do seem faster and are quite cool.
I think it would take a large sample to eek out any results of an fps test such as done in the Bowyers Bible.
Craftsmanship and design are much greater factors than limb length alone. The shooter is also a huge part of a bows ultimate performance.
Title: Re: WHY are short bows slower?
Post by: Del the cat on March 11, 2011, 04:13:55 pm
"One of the cruel realities of bow design is that shorter straight bows can't be as fast per pound as longer straight bows even at equal draw length.  Bewteen 35" and 60" possible performance rises roughly 1 fps per inch of bow length.  Cast rises slowly from there to around 68" then only minor improvement from there to 80" and only then if given a more elliptical tiller."

-Tim Baker
Traditional Bowyer's Bible IV
Yeah but you are changing the rules here and suddenly taking 60" as your reference.... like pulling a rabbit from a hat.
"lies damn lies and statistics" as the famous qoute goes.
From my ELB based view as you reduce length from say 74" you do get faster... indeed having built a 89" longbow I can assure you that longer gets slower.
It all depends on where you take your start point in terms of length.
The real problem is a badly worded post in the first place.
'Shorter' is meaningless without a reference.
Del
(Grumpy cat ;))
Title: Re: WHY are short bows slower?
Post by: George Tsoukalas on March 11, 2011, 04:27:01 pm
A 52" bow drawn 26" will stack and take a lot of set.  Jawge
Title: Re: WHY are short bows slower?
Post by: NTD on March 11, 2011, 04:51:30 pm
Del,
35-60"  You cherry picked the 60".  And these aren't my words they are Tim Baker's, maybe you missed the quotations ::)  He also goes on to say that cast only improves up to 80" IF if the tiller is adjusted.  So your example of an 89" longbow being a dog is probably quite accurate but hardly a repudiation of the quote. 

You also said that the original post is meaningless without a reference...Maybe cats have poor vision...he said 56" and 66"

A 52" bow drawn 26" will stack and take a lot of set.  Jawge


A bow made with stiff outer limbs and inner limbs wide enough to compensate for the extra work being done would not take excessive set or have stacking issues, especially at 26".  A molle design for instance...
Title: Re: WHY are short bows slower?
Post by: Del the cat on March 11, 2011, 05:38:02 pm
Post deleted...too grumpy ;D
Del
Title: Re: WHY are short bows slower?
Post by: Cacatch on March 11, 2011, 05:42:01 pm
Most of us shoot short arrows with short bows so the arrow weighs less than an arrow from a longer bow, thus compensating for some of the shorter power stroke. Also, shorter limbs take less time to snap back to brace position than longer ones do, causing the illusion that the arrow is going faster because it comes off the bow a fraction of a second earlier. Nonetheless, the power stroke is shorter, so they won't usually shoot as far or as fast as a longer bow, although they might appear to. That's my take on it.

CP
Title: Re: WHY are short bows slower?
Post by: Buckeye Guy on March 11, 2011, 06:45:13 pm
All this talk of cats and dogs and it aint even raining !!!
Title: Re: WHY are short bows slower?
Post by: JackCrafty on March 11, 2011, 07:43:38 pm
Short relative to what?  For a given draw length, there is an optimum bow length (or range of lengths) for maximizing the speed of the arrow. ;)
Title: Re: WHY are short bows slower?
Post by: nclonghunter on March 11, 2011, 07:50:22 pm
Just reading some this makes me wonder if the right question was asked. My understanding has to do with mass of bow and compression and tension woods. A long bow has narrow limbs and thinner vs. a shorter bow with wider limbs. I believe in The Bowyers Bible they actually weigh the bows to find the correct mass. Point is a short bow will shoot the same as a long bow if mass and design are correct.  I would say some short bows shoot faster than long ones if design is better and vice verse. If you have a bow that is slow then look at the design of it, that's where the difference is. I will say after you get to a certain length or shortness, you will be getting lower or greater than the "perfect mass" and design for a bow. If you can get a Bowyers Bible it will explain it far better than I can.
 
Title: Re: WHY are short bows slower?
Post by: Marc St Louis on March 11, 2011, 08:29:15 pm
Trying to sort this out while my short irons are still in the fire:

Say there are two well designed bows, one 66" the other 56". The 66" is straight and the 56" is reflexed enough to have a similiar F-D curve. However, it seems that even with less mass and no stack the short bows don't shoot faster. I can only guess that their less mass is cancelled out by the less leverage, correct? Is that the trade off or am I missing something else?

Thanks in advance, hopefully the next set of sticks I finish will be able to shed some light as well :)

Is this an assumption or empirical data?
Title: Re: WHY are short bows slower?
Post by: George Tsoukalas on March 11, 2011, 08:30:25 pm
I take that back. The bow I described will most likely break or be under drawn for its sort life. I do not like short bows. Can you tell? :) Jawge
Title: Re: WHY are short bows slower?
Post by: gmc on March 11, 2011, 08:33:17 pm
Can you post a picture of the unbraced profile and tiller of this slow "shorter" bow? Just curious, apart from giving up a little accuracy, the speed in comparison is too close to argue with.
Title: Re: WHY are short bows slower?
Post by: Jesse on March 11, 2011, 08:40:14 pm
I gotta say horse bows can hold their own in the speed department. As far as accuracy I prefer a longer bow. Besides extreme designs though I would say that @ a 28" draw the longer bows outperform noticeably for me. ------------ Not empirical data ::) 
Title: Re: WHY are short bows slower?
Post by: Ryano on March 11, 2011, 09:59:04 pm
Short relative to what?  For a given draw length, there is an optimum bow length (or range of lengths) for maximizing the speed of the arrow. ;)

I agree 100%
Title: Re: WHY are short bows slower?
Post by: Kegan on March 12, 2011, 12:14:40 am
Whoops, guess I was too vague :-X!

I don't have any bows to compare personally. But, looking at the numbers of well made bows out there and comparing the speed, they're all shooting more or less the same. My question is:

If a short bow has the same FD curve as a longer bow, but less mass, why is it NOT faster? Many of the well made bows all shoot around the same regardless of length. So if the short bow has less mass, it must be giving something else up and that is why they all shoot the same if well made.

The Mass principal helps show that all bow designs if well executed can shoot the same. I want to know why a bow with less mass is not faster than one with more mass. The more massive bow being longer, he only thing I see different- and this also form TBB vol. 4- being the longer, more massive bow has leverage to compensate for its mass. I wanted to know if there are things I'm missing or not aware of as well?

I guess "WHY aren't short bows faster?" would have been a better title. I'm trying to understand some of the physics behind all these awesome bows for reference. Just wnat to know how they 'tick' :)
Title: Re: WHY are short bows slower?
Post by: bow-toxo on March 12, 2011, 01:33:49 am
Trying to sort this out while my short irons are still in the fire:

Say there are two well designed bows, one 66" the other 56". The 66" is straight and the 56" is reflexed enough to have a similiar F-D curve. However, it seems that even with less mass and no stack the short bows don't shoot faster. I can only guess that their less mass is cancelled out by the less leverage, correct? Is that the trade off or am I missing something else?

Thanks in advance, hopefully the next set of sticks I finish will be able to shed some light as well :)

Howard Hill said ”The more a bow limb is bent, the faster it returns”. No one has mentioned the arrows. They have to be shorter for a short bow, and of course thinner for the sams draw weight as a longbow. They don’t have the mass to shoot a heavy arrow, therefore less penetration, but should shoot faster if the arrow length is proportional to the bow length.
Title: Re: WHY are short bows slower?
Post by: Traxx on March 12, 2011, 03:48:29 am
No one has mentioned the arrows. They have to be shorter for a short bow, and of course thinner for the sams draw weight as a longbow.

I assume then,that you are not familiar with the Archery,of the West coast Native people and how they applied it to their shooting.
Title: Re: WHY are short bows slower?
Post by: RyanY on March 12, 2011, 04:11:03 am
Kegan, I think your assumption that a short bow with the same FD curve shooting slower is wrong. The reason short bows don't shoot as fast as long bows is because they don't store energy as well so they have Different FD curves. If you have a short and long bow, same general design, pulling the same draw weight at the same draw length, the shorter bow will store less energy. If you could make a short bow store as much energy as a longbow, I imagine it Would shoot faster because of lower mass, if designed well enough to do so.
Title: Re: WHY are short bows slower?
Post by: Kegan on March 12, 2011, 11:00:55 am
Kegan, I think your assumption that a short bow with the same FD curve shooting slower is wrong. The reason short bows don't shoot as fast as long bows is because they don't store energy as well so they have Different FD curves. If you have a short and long bow, same general design, pulling the same draw weight at the same draw length, the shorter bow will store less energy. If you could make a short bow store as much energy as a longbow, I imagine it Would shoot faster because of lower mass, if designed well enough to do so.

That's exactly what I thought, but so far I've yet to see one that does shoot faster. Most of the examples of well made short bows (60" or less) all seem to shoot as fast as a longer bow. Even with FG, the short bows are not shooting the pants off their longer- and heavier- couonterparts. Even Asiatic recurve replicas, shooting same GPP and draw length, don't put some well designed longbows to shame.

It seems that if you have a bow that will survive with less mass and store more energy, it will be faster. Given the same length between two bows that seems very true, but when you reduce mass by shortenning the whold design the resulting short bow now seems to shoot about the same. Why is that? Why is it not faster?
Title: Re: WHY are short bows slower?
Post by: gmc on March 12, 2011, 11:49:41 am
I don't think you can compare the FD curve in your example as being the same as they will store energy differently. If we are talking about working vs. nonworking handles, the nonworking porition removed to achieve the shorter length, lower overall mass (which I think we are) then it will still take the same amount of working mass on both designs to deliver. The FD curve of the shorter bow will show a lower "early" draw weight but the longer power stroke of the shorter bow will make up a lot of ground in the end. It has been my my experience that the end result in speed is marginal in comparison between the two.

Designing for a slight bend in the handle section, holding the inner 3rd a little more rigid on the shorter bow, has delivered a faster result for me. I can use the best of both worlds, utilizing more working wood within a shorter length. The tiller is somewhere between circular and elliptical, and I find these bows are shorter and faster within the realm of what I build.

As you can tell, I do have a bias towards shorter bows and this is just my opinion based on what I've experimented with as shorter, faster bows, I do find intriguing.
Title: Re: WHY are short bows slower?
Post by: bucksbuoy on March 12, 2011, 01:43:34 pm
In theory shorter limbs should be faster. Longer limbs have more cast, better penetration, and longer range. I just think there are so many factors and variables that you cant change one without affecting another. Another thing Ive noticed is that most woods have a general window of speed and tend to shoot that speed no matter how the bow is built, to a degree, as long as it is built reasonably well. Hickory, osage, yew maybe around 150 fps? Maple, elm, other less dense woods around 190?
Title: Re: WHY are short bows slower?
Post by: NTD on March 12, 2011, 02:00:04 pm
Another thing Ive noticed is that most woods have a general window of speed and tend to shoot that speed no matter how the bow is built, to a degree, as long as it is built reasonably well. Hickory, osage, yew maybe around 150 fps? Maple, elm, other less dense woods around 190?

WHAT??? :o
Title: Re: WHY are short bows slower?
Post by: Traxx on March 12, 2011, 11:58:02 pm
Ill second that,WHAT??? ???
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 01:31:04 am
If shooting 10gpp at the same draw weight and draw length, best designed short bows won't shoot as fast as well designed longbows simply because they can't store as much energy. I think what happens is that, if you were able to get a short bow to store as much energy as its longer counterpart, the attributes which give that short bow more stored energy would also hinder its speed, most likely due to excess limb mass. I had a discussion on PP a while ago about bow mechanics and it seems that bow length is proportional to a certain arrow mass where if a longbow shoots a 10gpp arrow with a certain efficiency a shorter bow will shoot the 10gpp arrow with greater efficiency but less speed. Shooting the shorter bow with an arrow which brings down efficiency to the same as the longbow with 10gpp would raise speed to the same as the longbow with its arrow. Sorry if this explanation is confusing.

Bucksbouy, what you're saying about wood and speed is just wrong. This may be true if each wood is compared in one exact design but if each bow is designed to match the wood, all woods shoot equally well. Design is everything.
Title: Re: WHY are short bows slower?
Post by: Kegan on March 13, 2011, 03:34:40 am
If shooting 10gpp at the same draw weight and draw length, best designed short bows won't shoot as fast as well designed longbows simply because they can't store as much energy. I think what happens is that, if you were able to get a short bow to store as much energy as its longer counterpart, the attributes which give that short bow more stored energy would also hinder its speed, most likely due to excess limb mass. I had a discussion on PP a while ago about bow mechanics and it seems that bow length is proportional to a certain arrow mass where if a longbow shoots a 10gpp arrow with a certain efficiency a shorter bow will shoot the 10gpp arrow with greater efficiency but less speed. Shooting the shorter bow with an arrow which brings down efficiency to the same as the longbow with 10gpp would raise speed to the same as the longbow with its arrow. Sorry if this explanation is confusing.

All very true but not what I'm asking- or even arguing. I'm working under the assumption all that is understood and accepted. The shorter bow has a higher efficiency due to less mass. If you compensated for the lower stored energy by reflexing it why doesn't the short bow NOT outshoot the longer coutnerpart? Does the extra mass due to reflexing just cancel it out like it does in a longer bow or does the shorter bow lack leverage or is it something else entirely?

Is it all just about mass? If the short bow is reflexed enough to increase the stored energy does that extra mass now lower the efficiency down to longer bow levels? This wasn't something I accounted for, and I'm out of town so I don't have my TBB vol. 4 to review the Mass principal chart :( I'm asking an uneducated question... man I hate that.
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 03:47:07 am
I believe that is the case. I just think shorter bows can't be designed to store as much energy and handle the same draw weight and draw length as longer bows with out being over encumbered by the extra mass needed to do so.
Title: Re: WHY are short bows slower?
Post by: bow-toxo on March 13, 2011, 04:20:05 am
No one has mentioned the arrows. They have to be shorter for a short bow, and of course thinner for the sams draw weight as a longbow.

I assume then,that you are not familiar with the Archery,of the West coast Native people and how they applied it to their shooting.

 No, I'm not. Enlighten me.
Title: Re: WHY are short bows slower?
Post by: bow-toxo on March 13, 2011, 04:36:05 am
I believe that is the case. I just think shorter bows can't be designed to store as much energy and handle the same draw weight and draw length as longer bows with out being over encumbered by the extra mass needed to do so.

   I don’t understand . The  energy stored by any bow would be the energy needed to pull it to full draw. How would that be different in two bows of equal draw weight but different lengths ? Also, would a lighter arrow be faster than a heavy one, at least on a bow of less than warbow draw weight ?
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 04:46:45 am
bow-toxo, two bows of the same draw weight and draw length can store different amounts of energy depending on their design. Draw weight doesn't equal energy storage. This is why recurves can store much more energy than straight bows and have the potential to shoot faster. It has to do with how the string pulls on the limb. I'm sure we can all agree that short bows stack earlier in the draw than longbows and this is because a longer bow allows the string more mechanical advantage at higher draw lengths. FD curves show the difference in energy storage where a longbow may be a straight line to its desired draw weight the short bow would be a curve below that line. It still ends up at the same draw weight but the space between the lines is the difference in stored energy. This is hard to explain because I don't fully understand exactly how the mechanics of string angle affect stored energy and that all this would be easier explained with graphs.  :D
Title: Re: WHY are short bows slower?
Post by: Kegan on March 13, 2011, 10:51:19 am
I believe that is the case. I just think shorter bows can't be designed to store as much energy and handle the same draw weight and draw length as longer bows with out being over encumbered by the extra mass needed to do so.

That makes sense. My original example completely overlooks all the mass needed to get the 56" bow to hold severl inches of reflex. In which case the short bow would be function more like a longer bow: higher stored energy but with lower efficiency due to mass.

Thanks for the help :)
Title: Re: WHY are short bows slower?
Post by: Badger on March 13, 2011, 11:12:34 am
      Flight bows are very short bows, they tend to store good energy for their length but really capitalize on being more efficient. Generaly speaking what we make are hunting bows that shoot hunting weight arrows, 10 grains of arrow weight per pound of draw weight and a 28" draw are used as a standard for testing. Recurves around 60" long tend to be the fastest here give or take a bit and longbows at around 66" to 68" tend to be the faster ones. Designs are still actively being improved upon for the flight bows as no limit is put on how light an arrow can be, the length of an arrow they use is 23" so usually about 150 grains is about the lightest we can get them and still maintain enough stiffness to shoot straight. The lighter the arrow is the more the bow tends to rely on efficiency based on "virtual bow mass". Likewise if a bow were required to shoot extremely heavy arrows designs would get longer and bows would rely more on pure energy storage. Mark St Louis has become very good at redcucing outer limb mass in his recurves as is rewarded with the best of both worlds getting high energy storage as well as high efficiency. Longbows and R/D bows have gone more elyptical in the tiller effectively shortening the working limb and have gained a lot of performance here in recent years.
Title: Re: WHY are short bows slower?
Post by: Kegan on March 13, 2011, 11:50:57 am
Thanks Steve! How big a difference is there in speed between flight bows and "hunting" bows at 10 gpp?
Title: Re: WHY are short bows slower?
Post by: Eric Garza on March 13, 2011, 12:06:40 pm
...FD curves show the difference in energy storage where a longbow may be a straight line to its desired draw weight the short bow would be a curve below that line. It still ends up at the same draw weight but the space between the lines is the difference in stored energy...

Not always.  Here is an FD curve i made of a short, 47 inch hickory bow that i finished last year and traded.  As you can see the FD line is a curve, but it curves above the line connecting brace height (0 pounds draw) to the final draw weight of about 59 pounds at 23 inches.  If you compared this line to the straight line connecting brace height to full draw it would show that you have stored more energy.  The bow was 3 cm wide at the handle and tapered to 1 cm nocks, if my memory serves me.  No Eiffel Tower shape to the limb tips.

http://www.uvm.edu/~egarza/47_Inch_Hickory_FD.jpg
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 01:54:53 pm
Eric Garza, I agree that my said example is not always the case but say your bow was drawn to a full 28". If a straight bow it would most likely take a large spike in the last few inches of draw where a longer bow would not, yielding more stored energy. Also, although it has a good FD curve, the curve shows nothing in the way of speed.
Title: Re: WHY are short bows slower?
Post by: Jesse on March 13, 2011, 01:56:55 pm
I have also noticed that a short working limb on a longer bow seems to be a great combination of speed and shootability. Here is a picture of a fdc of Kens bow. Ken lives real close to me and has been helping me out with my bow building. As far as I know he made the fastest bow officially tested at WTT.  @ 199.7 fps 10 gpp @ 28" draw . There where a lot of bows real close in speed and some recurves were even right up there. I guess it comes down to personal preference. I seem to like the feel and shoot the best with a 64" to 68" longbow. :)
(http://i168.photobucket.com/albums/u169/WIbowyer/1_kenro_reaper_hotrod_fd-1.jpg)
Title: Re: WHY are short bows slower?
Post by: Eric Garza on March 13, 2011, 03:52:49 pm
Eric Garza, I agree that my said example is not always the case but say your bow was drawn to a full 28". If a straight bow it would most likely take a large spike in the last few inches of draw where a longer bow would not, yielding more stored energy. Also, although it has a good FD curve, the curve shows nothing in the way of speed.

The bow was originally straight, but took perhaps 3/4 an inch of set by the time it was shot in and I measured its FD curve. 

Do you mean to say that the short bow's FD curve would spike towards 28 inches and yield a sudden rise in stored energy?  I can't easily interpret what you're trying to say. 

And of course you're right, the FD curve says little about arrow speed.  It tells us how much energy the limbs store, but not necessarily how much they can deliver into the arrow upon release.  Release style and quality have a lot to do with that, as well as string weight and other things.
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 05:27:38 pm
Well say you built the bow to draw to 28". The FD curve would be shallow to a certain point and raise suddenly in the last few inches of draw to reach the full draw weight (this is what we know as stacking). This curve would be below a straight line curve produced from a longer bow thus storing less energy.
Title: Re: WHY are short bows slower?
Post by: crooketarrow on March 13, 2011, 06:13:24 pm
   If mass is equal to the design stored engery in the limb the longer the limb the more stored engery. The more efectively the engerys put into the arrow =ing more speed. Not sure if that makes sence. Way to many vairables and WAY OT TECTIAL FOR ME I build selfbows.
Title: Re: WHY are short bows slower?
Post by: bow-toxo on March 13, 2011, 08:36:30 pm
      Flight bows are very short bows, they tend to store good energy for their length but really capitalize on being more efficient.                                                                                                               ,
So if longer bows store more energy and shoot faster, why are flight bows shorter ?
Title: Re: WHY are short bows slower?
Post by: RyanY on March 13, 2011, 08:56:57 pm
Flight bows shoot light short arrows. Shooting a shorter arrow means that the bow doesn't have to worry about stacking and can store sufficient amount of energy. They are also more efficient than longbows shooting lighter arrows because the limbs have less mass and they have a shorter string. Short bows thus have a faster dry fire speed at a shorter draw length than longbows do because less wood is moving. I think that's why.  :P
Title: Re: WHY are short bows slower?
Post by: Eric Garza on March 14, 2011, 12:20:12 am
Well say you built the bow to draw to 28". The FD curve would be shallow to a certain point and raise suddenly in the last few inches of draw to reach the full draw weight (this is what we know as stacking). This curve would be below a straight line curve produced from a longer bow thus storing less energy.

So an "S" shaped FD curve, starting above the line and moving below it before rising back up to it?  I've made several short bows and have plotted FD curves for pretty much all of them, and have never seen an FD curve turn out like the one you're suggesting.
Title: Re: WHY are short bows slower?
Post by: RyanY on March 14, 2011, 12:28:47 am
The curve wouldn't be S shaped but just a curve below the straight line. I haven't plotted enough FD curves to witness this but I'm referring to the FD curves as seen in TBB volume 1 which shows exactly what we're talking about with regards to stored energy and bow length. What it shows is that a longbow shows an even increase in draw weight through out its draw length. The short bow shows a low increase in draw weight earlier in the draw and then increase in draw weight later in the draw.