Bows:From the Ground Up

[benz72]

any possibility of an app? spreadsheet or other?

[Nymdok]

For Frost and Anthony:

What makes sense and what does not is not really to be judged. The data stands as is. The evidence indicated by the bows salvaged from the Mary Rose wreckage and others attests to the Size and Shape and Composition as well as other found bows.

As far as how we know they worked, I appeal to the persistent nature of Physics. If we take the same wood and the same dimensions in the same shape (the relevant variables) then we should get the same results today as we did back then.(In other words, the physics is the same 500 years ago as it is today.)

To be honest, I dont know when Europe began adopting other bow compositions and designs, that is why I allow the cross section as an OPTIONAL rule. Feel free to change the efficiency percentages. Feel free to leave it out all together.

I stand by the principles that some designs are more efficient at trasfering energy to the Arrow than others, and the english longbow is a poor design compared to the rectangular cross sectioned or 'flat' bow.

Nymdok.

[Nymdok]

Originally Posted by benz72

any possibility of an app? spreadsheet or other?

Sure benz...what did you have in mind? I have a spreadsheet that contains ALL my data and the formulas in them to generate. If you'd like, I suppose I can host it on my google site. Ill need some time to clean it up a bit, but in the interim You can see that the math is pretty simple.

Nymdok

[Anthony]

Originally Posted by Nymdok

As far as how we know they worked, I appeal to the persistent nature of Physics. If we take the same wood and the same dimensions in the same shape (the relevant variables) then we should get the same results today as we did back then.(In other words, the physics is the same 500 years ago as it is today.)

True, but I have some doubts as to the degree to which wood and dimensions are actually the same, and arrow weight also plays a major role in efficiency. There is little question that self bows (including longbows) were less efficient than composite bows, let alone compound bows, but I think the difference is being overstated here.

Incidentally, the reason for the D shape of the yew longbow has to do with limitations of the bow material. You want heartwood for the back of the bow, sapwood for the front of the bow. To accomplish this, you take a stick and split it in two. This results in a D shape.

[DanHoward]

Yew is a strange wood. Its sapwood is good at tension while the heartwood is good for compression. It has similar mechanical properties to a composite bow - though less efficient. That is the reason for the D-section. You can't effectively incorporate both the heartwood and sapwood in a flat bow. I doubt the D-section is as inefficient with yew as it might be with other woods.

Edit: heh, Anthony posted first.

[Nymdok]

Originally Posted by DanHoward

Yew is a strange wood. Its sapwood is good at tension while the heartwood is good for compression. It has similar mechanical properties to a composite bow - though less efficient. That is the reason for the D-section. You can't effectively incorporate both the heartwood and sapwood in a flat bow. I doubt the D-section is as inefficient with yew as it might be with other woods.

True, Yew is sort of a natural Composite in that sense, but I doubt that Yew as a species has biologically evolved to the point that it is that different from the Yew used back then. I believe I understand why they used the D shape, however, it doesnt change the design flaw.

Originally Posted by Anthony

True, but I have some doubts as to the degree to which wood and dimensions are actually the same, and arrow weight also plays a major role in efficiency. There is little question that self bows (including longbows) were less efficient than composite bows, let alone compound bows, but I think the difference is being overstated here.

Increase Arrow weight versus the virtual mass of the bow does increase efficiency. Basic Set however only lists ONE arrow weight. (.1# or 700 grains) . What that means is that we all work to that standard.

From Klopsteg:

If the Virtual Mass of the bow equals the mass of the arrow the efficieny is about 50%.
If the Virtual Mass is about 1/3 the mass of the Arrow, the efficiency is about 75%. (physics of Sport pg15)

http://www.google.com/search?hl=en&q...cy&btnG=Search

The physics of sport is also a Klopsteg book.

Since we are all shooting the same mass arrow, then to assume that the Longbow, with its much higher virtual mass, is less efficient than the Rectangular flatbow (note it is also a self bow) with its much lower virtual mass, I think is a fair and reasonable to accept his denotations of 40%-80%.

Again, you may wish to alter it to suit your taste 60-80% or 3/4 or however you wish. Or omit it entirely.

Nymdok

[Anthony]

Originally Posted by Nymdok

Since we are all shooting the same mass arrow, then to assume that the Longbow, with its much higher virtual mass, is less efficient than the Rectangular flatbow (note it is also a self bow) with its much lower virtual mass, I think is a fair and reasonable to accept his denotations of 40%-80%.

If we assume his 75% bow has virtual mass = 1/3 arrow mass, and that a longbow is twice the mass of an equivalent flat bow, you wind up with a 60% efficient longbow. To get the longbow down to 40% requires a bow that is 4.5x heavier.

It's possible that a D-shaped bow is twice as heavy, though I doubt it. It's grossly unlikely that it's more than 4x as heavy.

[DanHoward]

Originally Posted by Nymdok

True, Yew is sort of a natural Composite in that sense, but I doubt that Yew as a species has biologically evolved to the point that it is that different from the Yew used back then. I believe I understand why they used the D shape, however, it doesnt change the design flaw.

Of course the D-section is less efficient than a flatbow. But this is at least partially compensated for by the material (i.e. yew). Using a D-section will reduce effieiency but making it from yew will increase it. It is a trade-off. You can't make a flatbow and get the advantage of yew's properties.

[whswhs]

Originally Posted by Nymdok

Increase Arrow weight versus the virtual mass of the bow does increase efficiency. Basic Set however only lists ONE arrow weight. (.1# or 700 grains) . What that means is that we all work to that standard.

I don't see any reason that the standard rules couldn't add alternate arrow types with different weight and corresponding different range.

Bill Stoddard

[Anthony]

Speaking of which, range of arrows:

The kinetic energy of an arrow is 1/2 * m * v^2
The drag of an arrow is 1/2 * rho * v^2 * Cd * A (rho = atmospheric density; Cd = coefficient of drag; A = cross-sectional area).
Thus, drag is equal to KE * rho * Cd * A / m

Now, drag results in loss of KE; specifically, the loss of KE is equal to drag * distance. Thus, we can say dKE/dd = -KE * rho * Cd * A / m. As all terms are constant, this is simple to solve for KE; specifically, KE = KE(initial) * e^(-1 * d * rho * Cd * A / m). If we assume that 1/2 range is the range at which velocity is halved (and thus KE is 1/4), we can determine that 1/2D range is equal to ln(4) * m / (rho * Cd * A). Solving the actual aerodynamics is tricky, but mostly doesn't matter, because we can already see one important factor: 1/2D range is unaffected by speed.

As an interesting side point, we can figure out terminal velocity based on 1/2D. If an arrow has a terminal velocity Vt, we know that drag = G * m * (V / Vt)^2, or drag = G * 2 * KE / Vt^2, and 1/2D range is equal to ln(4) * Vt^2 / (2*G). If we assume a terminal velocity of 120 fps, 1/2D = 1.38 * 14400 / 64 or 310 feet.