The Effect of Heavier Badminton Racket Head on a Shuttlecock’s Velocity

Introduction

In badminton, the power of a smash depends on many factors, the main factor being the human fact, the technic, ability, and skill of the player. However, the racket also plays a part in the power of the smash. When a player does a jump smash, the strongest type of smash in the game, the momentum in the forward swing and the weight of the head of the racket along with swing technic/speed allows the racket the bend, known as flex, to increase the power of the smash. The ability to flex the racket is essential in badminton. Although flexing the racket and generating power is greatly dependent on the player, the balance of the racket is also important. There are 3 types of balances for badminton rackets: head heavy, head light, and balanced. Head heavy means that the weight distribution is more towards the head of the racket. Head heavy rackets allows the player to generate more power since there is a higher net force on the shuttle at point of impact, assuming that the acceleration of the racket is constant. In this experiment, the relationship between the mass added to the head of a badminton racket and the velocity of the shuttlecock will be investigated.

The velocity of the shuttlecock depends on the power transferred from the racket to the shuttlecock, in this case the momentum. Momentum is the mass times velocity of a moving object. In a closed system, the law of conservation of momentum states that the momentum from the racket is transferred entirely to the shuttlecock. Thus according to this, the in order for to maximize the momentum mass should be low to increase the velocity of the racket when swung. However, it is more advantageous to have a head heavy racket rather than a head light racket in order to increase force at the moment of impact between the shuttlecock and the racket. Therefore, since momentum of the racket is its velocity times its mass and momentum of the shuttlecock is its velocity times its mass, due to the law of conservation of momentum the momentum of the racket should equal the momentum of the shuttlecock giving the two equations below:

vs ms=vr mr

vs=vr mr

ms

In the two equations above vs is the velocity of the shuttlecock, vr is the velcoity of the racket, mr is the mass of the racket, and ms is the mass of the shuttlecock. In this case, the velocity is assumed to be constant as the shuttle will be hit with by one player with a full rotation jumps smash and at maximum. The relationship between the mass of the racket and the velocity of the shuttle is predicted to be an inverse exponential relationship, under the assumption that the mass http://www.badmintoncentral.com/forums/showthread.php/71019-The-physics-of-badminton-

What-gives-Badminton-rackets-their-powerhttp://en.wikipedia.org/wiki/Power_(physics)#Mechanical_powerhttp://en.wikipedia.org/wiki/Momentum#Conservation_of_linear_momentumhttp://www.yonex.com/z/http://english.people.com.cn/200505/14/eng20050514_184991.html

Equation 1

Equation 2

of the shuttle and velocity of the swing remains constant. There will a different limiting factors on the maximum velocity of the racket. In 2005, the fastests recorded ingame smash by Fu Haifeng at 332km/hr.

This idea is significant in development of rackets for sport equipement bussinesses since badminton is one of the fastest sports in the world in often using powerfull and fast shots to overpower the opponent’s defence. The head heavy and power aspect of a racket is often used in advertisment for companies such as Yonex in marketing their new products, often advertising that the head heavy nature delivers better and more powerful smashes, such as the new racket The Voltric Z Force in the head heavy based racket line.

Method

Figure 1: Diagram of set-up (top view)

Figure 2: Picture of lighting set up

Spotlights Person C (Siripong)

Person A (Jetro)

Person B (Mel)

Figure 3: Racket Specifications, total racket length 675mm

Figure 3

The racket is the constant of this experiment. These are the specifications of this racket:

Brand: Victor

Model: Meteor X80

Stiffness: Extra stiff 5/5

Head Heaviness: Head heavy 4/5

Grommet holes: 80

Strings: Yonex Nanogy 95

Tension: 24 lbs. all around.

Grip: 1 layer Yonex Supergrap as over grip

Grip: 165mmShaft: 216mm

Shaft+ Cap: 260mm

Head Racket: 250mm

Variable Measurements/ControlIndependent Mass added to racket head (Clay + duct tape)Dependent Velocity of racket (taken with high speed camera at 1000fps)Control Same person smashing (Jetro Pirasmepulkul: Varsity Badminton

player + IASIS) Same racket. Method of stroke: Full rotation, Maximum swing, Full jump smash.

Swinging arm and racket as fast as possible. Same brand of shuttlecock (Yimnex) Location the shuttle was served relatively to the same position as

shown by the green circle in Figure 1.Table 1: Variables

The experiment was conducted in the following steps:

1. Set up court as shown in Figure 1 and 2.2. Both players (A and B) stretches and rally to warm up muscles3. When warmed up, retrieved a new shuttlecock and mass both shuttlecock and racket with

an electronic balance.4. Person C stands on top of the table behind the spotlights to ensure that camera height is

leveled with where the shuttle will be smashed.5. Person C records with high speed camera at 1000 frames per second6. Person B serves the shuttlecock with a full underarm forehand serve to green circle

indicated on Figure 1. 7. Person A does a full straight jump smash back to Person B’s position.8. Person B leaves the shuttle to fall to the ground.9. Person B retrieves the shuttle and serves again in the same manner as step 6.10. Steps 6-9 is repeated 4-5 times since more repetition will increase level of fatigue in both

players affecting accuracy of serve and power of smash.11. The used shuttle cock is massed again for final mass and the shuttle is marked with W-0.12. Both players rest and hydrates.13. A strip of duct tape is placed directly on to the top of the frame between the 11 o’clock

and the 1 o’clock position and middle of tape at 12 o’clock; the strip should be no longer than 10 centimeters. The strip should be massed before application to racket.

14. Warm up using original warm up shuttle to get accustomed to new racket mass.15. When ready, retrieve new shuttle and repeat steps 3-12.16. Mass a strip of clay and duct tape and apply them in the same manner as step 13.17. The repeat steps 3-12 again for a total of 6 different racket weights.18. It is recommended to not exceed 10 grams off added weight to head since depending on

racket stability and strength the racket.

The independent variable, weight added, ranges from 0grams to a total of 9.59grams added to the top of the racket over 6 different weight intervals, and 4-5 smashes per weight examining each smash to pick 3 of the best ones for video analysis. The last two weights were added using clay and duct tape. The dependent variable was measure with video analysis from a video taken at 1000fps.

Controls

The shot technic was hit by the same person, Person A, Jetro. He is an experienced badminton player that can control the technic to keep it constant and ensure full transfer of power. The shot is a full jump smash with complete shoulder rotation hitting the shuttle at highest point. The service technic was also kept constant using a forehand underhand full serve. This allows minor variation to the point to the position of the shuttle when it reaches Jetro.

The shuttles were massed before and after each video. The integrity of the shuttle is important to maintaining its velocity, as the feather changes with every shot. Thus to ensure that the shuttle is as little damaged as possible for each mass, Person B, the server, does not receive the shuttle after each smash.

The same racket was used throughout the experiment since the specifications of each racket, even if it is the same make and model will vary, although the difference may be negligible to players. However, changing the racket either between 4U and 3U (each U’s have different mass) or changing the model or the brand completely will affect the feel for the racket and velocity. This racket is chosen because this is the smasher’s racket of choice. He is most used to the feel of this racket and thus can deliver a full smash hitting the “sweet spot” to ensure maximum transfer of momentum.

Data Collection and Processing

Mass of Racket (±0.01g)

Mass Added to Head (±0.01g)

Velocity recorded without conversion (±0.05m/s) Average Velocity

(±0.09m/s)Trial 1 Trial 2 Trial 3

94.82 0.00 1.80 1.82 1.86 1.83

96.45 1.62 2.41 2.49 2.39 2.43

97.48 2.65 2.62 2.58 2.45 2.55

98.26 3.44 2.73 2.77 2.72 2.74

98.37 5.49 2.81 2.78 2.71 2.77

104.41 9.59 1.66 1.60 1.52 1.59

Table 2: Raw Data

Table 2: For masses 3.55 and 6.56 grams, clay and duct tape were added to the frame. The uncertainty for velocity of each trial is estimated to be approximately 0.05m/s or 5cm/s. This

uncertainty comes from scaling the racket in the video. The velocity values for each trial were obtained through analysis of the video take with a high speed camera. The velocities for each trial are velocities without conversion from 1000fps (speed of camera) and 30fps (speed of video played on computer). Sample graph shown below:

Figure 4: Sample Graph

Figure 4: Sample graph for mass 2.65±0.01g Trial 1. In the video frame shown above, the green represents a scale in the video. The green line marks the length of the shaft of the racket, from the T-joint to the bottom of the cap at the start of the grip, 0.252m long. The blue dots mark the path of the shuttle over 7 frames. The perpendicular yellow lines are the set origin so that the x-axis, horizontal yellow line, is parallel to the path of the shuttle so that the velocity can be determined. In the graph, the red dots correspond to the blue dots in the video frame. Each red dot represents the shuttle’s position at a specific time. The slope linear fit over the 7 positions is the velocity of the shuttle after the smash.

Table 3: Converted Velocities

Mass Added to Head (±0.01g) Converted Average Velocity (±10km/h)

0.00 2201.62 2902.65 3103.44 330

Table 3: The converted average velocity is the original velocity in m/s from the video multiplied by 3.6 to convert to kilometers per hour and then by 33.3 to account for the difference in frame rates of the video watched at 30fps and the rate that the video was taken, 1000fps.

5.49 3309.59 190

Figure 5: Mass Added and Average Velocity

Figure 5: The relationship shown above between the mass added and the shuttle velocity is represented as a Natural exponential relationship. It can be seen that the last data point is significantly different from the others and this is not included in the curve fit. The equation of the

relationship is given bellow:

v=(−120 ±10 ) e(−0.6±0.1 ) m+(338 ± 9)

The variable v represents velocity in kilometers per hour and m represents mass added to the racket.

Sample Calculations

Calculation for Average velocity for mass 2.65±0.01g

Average=T 1+T 2+T 33

Average=2.62+2.58+2.453

=2.55m /s

Uncertainty Calculations for average velocity for mass 2.65±0.01g

ua=Range

2

Equation 3

ua=2.62−2.45

2=0.085 m /s

ua=0.09 m /s

Average=2.55 ± 0.09 m /s

Conversion from m/s and video frame rate conversion for mass added 2.65±0.01g

2.55 ms

×3.6 ×33.3=305.7 kmhr

Uncertainty of km/h for 2.65±0.01g

0.09 ms

×3.6 ×33.3=10.799

u=310 ±10 km /hr

Conclusion

From the results of this investigation it can be concluded that the velocity of a shuttlecock will increase as mass on top of the racket head increases. However, above a certain mass the racket velocity should remain steady. This results confirms the prediction that the velocity should increase at a decreasing rate and plateau above a certain mass. This relationship is modeled by a negative exponential relationship and the equation is represented by equation 3, reproduced below:

v=(−120 ±10 ) e(−0.6±0.1 ) m+(338 ± 9)

The main number of importance in the equation above is the coefficient of m. This value indicates the general trend for this person showing the rate at which the velocity levels off. During the section in which the velocity is increasing, this indicates that the limiting factor affecting the velocity is the mass of the racket head. This means that as the player is swinging at the maximum velocity yet the velocity of the shuttle does not increase because the racket was too light and thus the momentum is limited. However, at a certain mass in this case at 3.44g, the limiting factor becomes the speed of the contraction of the person’s muscles.

The level of confidence in the data is relatively low due to the large uncertainty bars on each data point. However, the confidence in the curve fit is relatively high since the curve passes through all the points within their uncertainty levels.

In this case, Equation 3 is only applicable to this particular situation and this particular player since each player’s muscle anatomy is different and their conditioning varies. However, the general form, shown below applies to all rackets and to all players.

Equation 3

Equation 4

v=A e−Cm+B

Equation 4 shows that a certain mass the velocity will reach a plateau since the limiting factor will change from the mass applied to the racket to the muscle contractions of the player propelling his arm and swinging the racket. A further prediction can be made that the velocity of the shuttle will start to decrease over a point since the muscles will require more and more energy to move a heavier racket through the air and to swing the racket fast enough to maintain constant velocity.

Evaluation

One of the sources of error in this investigation is represented by the last data point in Figure 5 and Table 3 for the largest mass added. This value was excluded from the curve fit since Person A, the smasher, specifically stated that he was holding back on his swing due to his fear for the integrity of his racket. Also the clay and the tap fell off the racket during the experimentation. The confidence in the integrity of the racket will always be a factor since above a certain mass the player will feel the flex of the racket to a point where they may thing that the amount of stress put on the racket may force it to crack or break. This could be improved by telling the player not to hold back and that his racket will be compensated for if broken. If the racket does break however, changing the racket used in the investigation will change the conditions of the experiment and the racket will no longer be a control factor. However, the player holding back on his swing and not reporting it will be more damaging to the results compared to changing the racket.

Another source of error is fatigue. In this investigation, fatigue factor was attempted to be controlled by only doing 4-5 smashes in succession and taking plenty of time to rest in between each video. However, by the end of the investigation, it was clear that both Person A and B were tired, thus it can be assumed that fatigue would have affected the rate of increase of velocity making each successive mass added. It can also be assumed that the velocities of each mass maybe higher if they were done at the lowest level of fatigue. A method of improvement is to have each mass added done with a long break for rest and hydration in between and also it would be good to monitor the smasher’s heart rate to make sure that it returns to his normal heart rate (normal= before first experiment) and rest longer after that to ensure muscle recovery.

Another point of error is the feathers on the shuttlecock, after each hit on the shuttle’s feather will be affected and some could break if the ends were to get caught in between the strings. In this investigation, only one shuttle was used for each mass added. The shuttle was smashed 4-5 times thus it was hit between the two players 8-10 times. Each hit will already degrade the conditions of the shuttle thus each hit will affect the velocity of the shuttle by changing its stability, velocity, or the amount of recovery time from when the shuttle impacts the racket when it takes on this normal path. Just after the point of impact, the shuttle will have its head upwards and the feathers will have an effect on the time for the shuttle’s head to begin facing downwards.

A method of improvement is to use new shuttles with every hit and in order to decrease the amount of players hitting at the shuttle could be dropped or thrown from a high point instead of served.