10 bows . Lots of ?

[Selfbowman]

I have built 10 or so bows in the last couple months. All but one is 69" ntn. The other is 67". I have weighed them with a scale when finished. My ? Is how does the math work out on these and which one should have the best cast according to the math.  I will post a pic of the bows and weights.

[Badger]

   You would need the starting reflex in the bow as well as the stiff area near the handle and the stiff area near the tips to project a mass weight by my calculator. In most cases the bow that finished closest to it's starting profile would win out assuming they all had similar starting profiles. Outer limb mass would also be a contributing factor or course.

[Selfbowman]

All bows came off of a caul that has 2 1/2-3 " of reflex.2 1/2 under handle 1 3/4 at mid limb and 1 1/4 at 8-9 from tip. They vary when coming off the caul somewhat usualy not losing more than a 1/2 a in. Then when tillered at 1 1/2-2" remain . After 500 arrows more set. Then it stops but is smooth and has good cast. Some are almost D bows, some flat pyramid bows , half breed meaning flattened D section at fade and more flat at mid limb. All I try to get the ends light as I dare. Most end up with slight reflex to flat at center and tips. Mid limb off the straight edge. Arvin

[Badger]

 Your bows all seemed to hold their profile very well and I know you mentioned once that you are getting about 200 yards with a 10 grain arrow which is excellent cast. Your mass weight seems quite a bit higher than normal but won't usually penalize your cast if it is on the inside limbs. I would rather have less set and more mass weight anytime.

[Philipp A]

Nice work! Little set on all of the bows. I am wondering which profile gave you the best cast and what thickness the bows were at fade, mid section and at the tips.

Happy New Year,

Phil

[Del the cat]

IMO the maths will tell you nothing.
Maths is a useful tool when applied to homogenous materials used in narrowly defined conditions.
Some rules of thumb and simplifed maths can provide some guidance, but I don't think it's much of a pedictor of anything unless your tillering is 100% consistent and I don't think many will claim taht with self bows.
I'm happy to be proven wrong, but IMO the time spent on maths would of ten be better spent running your fingers over the limbs.
My fave quote of 2016 was from Chris Boyton (a respected bowyer) I was discussing my Osage flight bow with him and saying I was wondering if I could maybe take some weight off the tips.
He said...
"You can always take more weight off tips"
The truth of this is obvious when I look over my bows, the tips get slimmer and slimmer as my experience increases.
Del
BTW Handsome looking bows.

[Badger]

 Del, working on English longbows I can take about 15 seconds before I start and run some numbers and know exactly what the bow will look like when I am done. Based on weight and what job the bow will be doing I can use the math to select the best wood for the job. Even though the math is more of a rule of thumb and not an exact science I guarantee it will get you close enough for an excellent start. Some experience does come into play with knowing what to do with the numbers.

[mikekeswick]

I once worked out the perfect taper rate for 72ntn elbs (from memory 0.009" taper), I generally used hickory back, boo cores (consistent weight and stiffness) and ipe bellies. I put all the taper into the cores, parallel back/belly lams and 12 - 16inch powerlam depending on weight. By adjusting the core thickness I could get within 5# desired weight most times and pretty much perfect tiller or very little work needed. It can be done by numbers but it didn't seem 'right' somehow

10 bows in a few months is good going! I would say that the one with the least handshock and least set will be the best

[Selfbowman]

Del I am not a math guy for sure . I do most by feel . I just thought the math wizards could give me a guess at my mass reduction and either tell me I was close or not to worry cause I was close enough. Just build the bows Arvin.  I love the challenge in every one. I have been working on this real dense bow also 69" 42@26 may have to cut this one off.its quick though. 500 gr arrow 175yd.

[Selfbowman]

Steve the mass may be in my handles. None are just alike but all very similar. All depends on the stave I make them a little thicker so I can cut my shelf in.

[Badger]

 Arvin, extra reflex requires more mass, extra mass in the handles you can allow for also. Doesn't take much in the handles to tack on a couple of ounces. I am a big believer anymore in having enough wood to get the job done. mass in the inner limbs just keeps the set down and doesn't hurt your performance. Your performance is great, if you had too much mass it wouldn't be great LOL. I usually finish a 66" osage with 2 1/2" reflex at about 21 to 22 oz. If you have a longer handle and fade area or stiff inner limbs more mass needed also. I don't use any number when building a bow except for projected mass.

[willie]

Selfbowman

very nice work, thanks for posting

[willie]

Steve

have you done a write up on the mass princilpe since the chapter in TBB? I know that your thinking has evolved some, but I could not find the formulas here at P.A. Seems like it should be a sticky in the "how to" section

[Del the cat]

Del, working on English longbows I can take about 15 seconds before I start and run some numbers and know exactly what the bow will look like when I am done. Based on weight and what job the bow will be doing I can use the math to select the best wood for the job. Even though the math is more of a rule of thumb and not an exact science I guarantee it will get you close enough for an excellent start. Some experience does come into play with knowing what to do with the numbers.

Yeah, I s'pose I'm being disingenuous as I do something similar...
But if you can do it in 5mins it's arithmetic not maths 
I s'pose I have a bit of a bee in my bonnet about maths, I'm ok to a point but dropped out of uni' 'cos I couldn't handle the higher maths, I was frustrated that I had better understanding of the physics than most but couldn't cut the maths... Sums me up, I'm an empirical guy.
I still have have a calculus book on the shelf that sits there accusingly.
Del 

[Badger]

Steve

have you done a write up on the mass princilpe since the chapter in TBB? I know that your thinking has evolved some, but I could not find the formulas here at P.A. Seems like it should be a sticky in the "how to" section

  Willie, I really haven't. I have almost quit making bows this year. The basic formula I had been using (which is not really math, it just amounts to placing a value on different parameters) has actually held up better than I expected it would. What I have done though is gotten better at applying it. Something I have thought about doing is going into more detail on how I use it to select woods and designs for a wide variety range of draw weights and draw lengths. I made up about a dozen ELBs last year with weights from 35# to 125#. These were all wood backed board bows. It really was interesting how I was able to use the mass weight to direct me in the tiller shapes and wood selections as well as finished bow lengths. really all aspects.