I added static recurves to the ends of a flat 35inch Hupa style bow, and the efficiency and arrow speed increased. It is a light weight experiment to explore the effect of add on recurves, and not a really serious bow, but the physical principals are still the same as for heavier bows.
The static recurves were added by gluing carved “siyahs” to the bow back, and then carving away the original bow tips to allow the string to flow smoothly off the tips. The nock to nock distance in a straight line was intentionally kept to exactly 35 inch to match the original bow length. This means that the string needs to be longer to wrap around the new curved ends of the bow, and forward to the recurved nocks. The recurves are 40mm high. (i.e. the nocks are 40mm forward of the back when the back is dead straight.). The bow was not re-tillered, except for adding the recurves, and carving away the old tips.
As expected, the stacking of the bow is significantly reduced by the addition of the recurves. This is due to lowering the draw force at and near full draw. Early draw weight was only marginally effected. The net result is a lower weight bow, with less stack, and less total energy stored. The flat version of the bow stored 7.8Ft-Lb. The recurved version only stores 7.2Ft-Lb.
The surprise is that the speed of a 170grain arrow increased from 92FPS, to 110FPS, in spite of loosing 8% in energy storage, and adding 23 grains to each tip. If the efficiency for various arrow weights is converted to virtual bow mass, the flat version has a virtual mass of 201grain, while the recurved version comes in at 126grain. If 1/3 of the string mass is deducted to get the bow only related part of this, the numbers are; flat version = 165grain, and recurve version = 100grain. The string weight difference is not nearly enough to explain the additional efficiency.
Original bow 35in long along the bow back nock to nock Bow mass 121g (not including string) String mass 7g (108 grain), length 34.3 inch Brace height = 93mm Draw force = 13.9Lb. at 21in. (7.8Ft-Lb. stored energy) 170 grain arrow = 92FPS. average (efficiency 44%) 543 grain arrow = 69FPS average (efficiency 78%)
Recurved version 35inch in a straight line length from nock to nock Bow mass 124g (not including string) String mass 5g (77 grain), length 35.25 inch Brace height = 93mm Draw force = 11.5Lb. at 21. (7.2Ft. Lb stored energy) 170 grain arrow = 110FPS. average (efficiency 63%) 543 grain arrow = 69FPS average (efficiency 82%)
The conclusion from all this is that there is more than just tip mass involved in efficiency. The tips are more massive, the draw weight is lower at full draw, the stored energy is less, but the light arrows still go faster.
« Last Edit: September 27th, 2005, 4:18am by woodbear »
Virtual bow mass is a fictional mass that accounts for the efficiency of a bow, in a manner that allows the speed of arrows launched by the bow to be calculated.
Think of a bow with a known draw-force curve, and efficiency with an arrow of a particular weight, say 500 grains. The area under the draw force curve represents the amount of work, or energy it takes to draw the bow. For instance, a very good 50Lb. bow might store 50Ft-Lb. of energy when drawn to 28 inches. If this bow is 60% efficient with the 500 grain arrow, 60% of the 50Ft-Lb of energy stored in the bow is converted to kenetic energy of the arrow when the arrow is released. That means 30Ft-Lb, of kinetic energy in the arrow, with a mass of 500 grains that equals 164 FPS arrow speed.
What happened to the 20Ft-Lb that did not go into the arrow? It remains in the bow as vibrations, and internal friction generated heat, etc.
How fast will a 400 grain arrow go with this bow? Virtual bow mass will enable you to calculate this.
Virtual bow mass is a fictional mass that we imagine as moving at the same speed as the arrow at the moment that it leaves the string, and having enough mass to account for the energy that is not in the arrow. In the example above, it will have to have 2/3 of the mass of the arrow, since the arrow has 30Ft-Lb of energy, and the virtual mass must have the other 20Ft-Lb. That means the virtual mass is 500grains*2/3 = 333grains. ..... If the Arrow mass is only 400 grains, the total mass (arrow and virtual bow mass) is 733grains. The arrow accounts for 400/733=55% of the total bow energy, or 27.3 Ft-Lb.
The 400 grain arrow speed is found by: speed = sqrt((E-arrow)/(m-arrow/(7000*2*32.16))) = 175 FPS
I hope this has explained the Virtual bow mass concept. It is in reality a measure of Bow efficiency as a function of arrow weight.
« Last Edit: September 28th, 2005, 4:13am by woodbear »
This is a comparison of the draw curves of the bow in both versions. Note that the recurves REDUCED the late draw weight but had almost no effect on the early draw weigth. I believe this is due to maintaining the straight line 35inch dimension from nock to nock, which effectively makes the bow longer as the string rolls off the recurves, and required a longer string. If I had maintained the string length instead of the straight line length, the early weigth would probably have been higher.
This last picture shows the two versions of the bow at full draw (21inch in this case). Note that the recurves have opened up the string angles, and the increased leverage has reduced the draw force from 14Lb, to about 11.5Lb. (This is my rationale for what can be seen in the draw curves above.)