PIGS AND PUMPKINS
Background info .:. Problem .:. Hypothesis .:. Variables .:. Method .:. Materials .:. Results .:.Video .:. Conclusion .:. Bibliography .:. Go Up
The
primary feature of a compound bow is the set of pulleys which both magnify the
force applied to the string and provide an advantage known as "let
off."3 A standard longbow requires
nearly as much force to hold it fully drawn as it does to draw it back. In a
compound bow, once the string is about 50-80% drawn, the pulleys absorb the
force with which the string is drawn; when fully drawn, little force is needed
to hold the string back.2 The cables and pulleys make
compound bows easier for the archer to use, but the real secret to its power is
in the composite materials from which it's constructed. The central part of the
bow is usually made of aluminium and the limbs are made of very strong but
somewhat flexible composite materials.1
More
traditional bows, such as standard and recurve bows, store the energy within
the actual frames and strings of the bows and require the same force with which
it was pulled back to keep it in that position. The central parts of the bows are
generally made of simple wood, and they are commonly coated with a clear finish
and a layer of fibreglass on the limbs in order to increase the bow’s integrity.
The average recurve bow is 48-70 inches long, and most of these types of bows
possess a draw weight between 15 and 25 lbs.1
When measuring the force curves of a standard, recurve, and compound bow, how does the design of each bow impact its force curve?
When drawing the standard and recurve bows, their force curves will increase directly proportional to their draw distances. However, due to the pulley system in the compound bow, the force curve will experience a significant decline when the pulleys activate, meaning that the bow will necessitate a lesser amount of force to remain drawn.
Independent: Draw Length
Dependent: Force
Control: Type of bow with respect to each set of data
In order to measure the force curves of both the standard and recurve bows, we will hang each bows from wooden supports with a meter stick placed perpendicular to the bows' drawstrings, which will be used to measure the draw length of each trial. Upon mounting the bows, we will proceed to hang masses from their draw strings, starting with 1 kg and increasing by 1/2 kg for each data point over a 14 kg interval. With each new mass, we will record the resulting distance the drawstring is stretched. Since the masses will be hung vertically, the forces will be calculated by multiplying each mass by the acceleration of gravity (9.81 ms-2). Above is a photo of the actual procedure being executed using a recurve bow with a 1 kg weight being placed on the drawstring.
v Compound bow
v Recurve bow
v Standard bow
v Wooden supports
v 90° clamps
v C-clamps
v Metal bars
v DUCT TAPE
v Meter stick
v Masses
v Force meter
v Logger Pro
v 3 pulleys
v String
Standard Bow |
|
Distance (centimeters) |
Force (Newtons) |
0 |
0 |
1.5875 |
9.81 |
2.2225 |
14.715 |
3.175 |
19.62 |
4.1275 |
24.525 |
5.08 |
29.43 |
6.0325 |
34.335 |
7.3025 |
39.24 |
8.255 |
44.145 |
9.525 |
49.05 |
11.1125 |
53.955 |
12.3825 |
58.86 |
13.6525 |
63.765 |
16.8275 |
73.575 |
15.24 |
68.67 |
18.415 |
78.48 |
20.32 |
83.385 |
21.9075 |
88.29 |
23.495 |
93.195 |
25.0825 |
98.1 |
26.67 |
103.005 |
28.575 |
107.91 |
30.7975 |
112.815 |
32.385 |
117.72 |
33.9725 |
122.625 |
35.56 |
127.53 |
37.1475 |
132.435 |
38.735 |
137.34 |
Compound Bow |
|
Distance (centimeters) |
Force (Newtons) |
0 |
0 |
8.5725 |
70 |
12.065 |
89.6 |
13.6525 |
107.8 |
17.78 |
119.7 |
17.145 |
115.5 |
22.86 |
101.5 |
29.21 |
77.07 |
30.7975 |
63 |
33.3375 |
73.5 |
24.13 |
100.8 |
26.67 |
95.9 |
32.385 |
68.6 |
28.2575 |
81.2 |
21.59 |
108.5 |
25.4 |
100.1 |
4.445 |
36.47 |
1.905 |
16.66 |
6.985 |
56.35 |
Recurve Bow |
|
Distance (centimeters) |
Force (Newtons) |
0 |
0 |
1.8415 |
9.81 |
2.794 |
14.715 |
4.064 |
19.62 |
5.334 |
24.525 |
6.2865 |
29.43 |
7.874 |
34.335 |
9.144 |
39.24 |
10.414 |
44.145 |
12.0015 |
49.05 |
13.2715 |
53.955 |
15.1765 |
58.86 |
16.764 |
63.765 |
18.3515 |
68.67 |
19.939 |
73.575 |
21.5265 |
78.48 |
23.114 |
83.385 |
24.7015 |
88.29 |
26.289 |
93.195 |
27.8765 |
98.1 |
29.7815 |
103.005 |
29.7815 |
107.91 |
32.9565 |
112.815 |
34.544 |
117.72 |
35.814 |
122.625 |
37.084 |
127.53 |
38.6715 |
132.435 |
39.9415 |
137.34 |
Our results suggest that the designs of both the recurve bow and the compound bow alter the force curve in a manner which significantly reduces the strain on the user drawing the bow when compared to the standard bow, which, to some degree, acts as a control for this comparison. This effect is optimized close to full draw, which is particularly noticeable in the force curve of the compound bow. The purpose of this is likely to allow users to aim more accurately and sustain a full draw longer without sacrificing much, if any, power.
It appears that our hypothesis is quite accurate for both the standard bow and compound bow, but inaccurate for the recurve bow. Instead of following a directly proportional pattern, the recurve bow's force curve begins with a concave-down curve and, after an inflection point at a draw distance of about 25 cm, ends with a concave-up curve. This is a result of its altered design and enables the user to exert less force than he/she would have had to with a bow that has a force curve similar to the standard bow. As we predicted, the standard bow nearly follows a direct proportion of 3.25 N/cm. It does, to a very limited extent, appear to have a curve to it not dissimilar in form to that of the recurve bow. This is likely standard for any bow (with the exception of compound bows) and due to its small magnitude, its significance is minimal. As we predicted, the compound bow's force curve significantly dropped as the pulleys activated. During the period they went into action (between 18 cm and 32 cm), the force required to hold the drawstring dropped by about 45 N (from 115 N to 70 N). After this point, the force continued to rise again, as should have been expected.
In the procedure for the recurve and standard bows, areas in which errors could have been derived from were minimal. The masses were assumed to have been manufactured precisely enough to make it acceptable to neglect any possible uncertainty. Similarly, the uncertainty pertaining to the distance of each trial’s draw length was seemingly insignificant; granted, human error still impacted the data (such as in the standard bow data at 30 cm), but such errors are difficult to measure, and they have little to no effect on the general outlook of the data.
The procedure for the compound bow contained a few facets that may have contributed errors to the data. For instance, the force meter that was used to measure the force during each trial fluctuated sporadically during the experiment; it is estimated that the force deviated as much as 7 N from the recorded data (1 N on the actual meter, but 7 N after accounting for the pulley system). Additionally, there were times when the pulley system that was used to draw the compound bow lacked enough integrity to stabilize the bow, and this may have further contributed to the uncertainty pertaining to the force recordings.
In order to improve the lab, one fundamental aspect that could make the data more precise would be to develop a more refined means of reading the distance of the draw length during each bows’ trials. For the compound bow’s procedure, resolving the issue pertaining to the force meter’s instability would yield better results. Also, using a force meter that would be able to support the entire force of the bow would make it unnecessary to use the pulley system, which would eliminate another source of error.
1 Jeffrey, Graeme. "Basic Bow Types." Centenary Archers Club. 1999-2008. Centenary Archers Club Inc. October 29, 2009. <http://www.centenaryarchers.gil.com.au/basic.htm>.
2 Nicholson, Joseph. “How Does a Compound Bow Work?” eHow.
October 29, 2009. <http://www.ehow.com/how-does_4568731_compound-bow-work.html>.
3 Walterscheit, Jen. “Selecting the Right Compound Bow for You.” 2008. Articlesbase. November 24, 2009. <http://www.articlesbase.com/sports-and-fitness-articles/selecting-the-right-compound-bow-for-you-498937.html>.
Related Websites
http://www.imagemet.com/WebHelp/spip.htm#force_menu.htm Taught us how to analyze force curves
http://mathewsinc.com/ Showed us different types of bows
http://www.hallmark.com/webapp/wcs/stores/servlet/SearchResultsView?Ntt=bows&gnav_go.x=0&gnav_go.y=0&Nty=1&storeId=10001&catalogId=10051&N=35&Ntk=all_fields&Ntx=mode%2Bmatchallpartial&RPP=12&SBQ=yes Taught us a lot about "bows" (and happiness)
http://www.maconlysource.com/Gallery/images/apples.jpg Great picture reference
http://www.centenaryarchers.gil.com.au/basic.htm MORE BOWS
http://www.ehow.com/how-does_4568731_compound-bow-work.html How compound bows work
http://www.articlesbase.com/sports-and-fitness-articles/selecting-the-right-compound-bow-for-you-498937.html More on compound bows