PIGS AND PUMPKINS

 

Background info .:. Problem .:. Hypothesis .:. Variables .:. Method .:. Materials .:. Results .:.Video .:. Conclusion .:. Bibliography .:. Go Up

 

 

 

 

 

Background Information:

 

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

 

 

Problem:

 

When measuring the force curves of a standard, recurve, and compound bow, how does the design of each bow impact its force curve? 

 

Hypothesis:

 

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. 

Variables:

Independent: Draw Length

Dependent: Force

Control: Type of bow with respect to each set of data

 

downsized_0106001600 (2).jpgMethod:

 

            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.

 

 

 

downsized_0115001652a (2).jpg0115001652 (2).jpg            For the compound bow, we will need to alter our procedure due to its unique draw system. Using an apparatus constructed out of metal bars and clamps, we will vertically mount the bow, and a meter stick will be placed parallel to the ground and adjacent to the bow as a means of measuring its draw length. We will use an electronic force meter to measure the force at any draw distance; however, due to a limitation on the capacity of the force meter, a pulley system must be used in order to divide the force being allowed to reach the force meter by 7. This will enable us to collect a sufficient amount of data that will be comparable to the other bows. Using the pulley system, we will manipulate the draw length of the bow and record the force that coincides with each point. The photo to the upper left shows the compound bow mounted to the metal apparatus using duct tape with the meter stick placed perpendicular to the drawstring. The second photo on the right illustrates the pulley system used to draw the bow; this is connected to the force meter, which is shown on the left of the photo.

 

 

 

Materials:

 

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 

 

 

Results:

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Data File : Text .:. Excel

 

 

 

Conclusion:

 

            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.

 

 

 

BIBLIOGRAPHY:

 

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