bigredlemon
Regular Member
Have you noticed how well your racquet performs changes from day to day, especially during swings of temperatures? As you know, the tension of the strings increases in colder surroundings because things shrink when it's cold
. I haven't been able to find an answer on exactly how much this change is, so I’m going to working out the physics problem here on BF. My physics is a bit rusty so point on any mistakes if you see one. I'm pretty sure I've got everything right though. If you aren't interested in the calculations, just jump to the bottom for the answer. (My feelings won't be hurt... not at all... sniff.)
Theory:
When temperature changes, the length of the string changes.
Since the string cannot shrink itself as it is tied at both ends, the net effect it an increase in tension as though the racquet was strung with shorter strings and pulled extra hard to make it fit on the racquet.
Since the effective tension at the point of impact is different from when the racquet is "resting," the effective tension of a racquet in a colder room will be dependent upon the effects of the shift of the "resting" tension. A look from the stress-strain curve of Nylon 6 shows that an increase in stress will cause a greater proportionate percentage change in strain. This means the greater your default tension is, the greater the percentage effect this will have. Hence, racquets strung at high tensions are much much much more vulnerable to this temperature change phenomenon. Since I've never studied engineering, I'll just pull a fast one for this calculation and tell you that this phenomenon doesn't exist.
The numbers:
I wasn't able to find the actual specifications of badminton string, presumably because it is an industry secret, so I’ll be working with the closest polymer that's in the public domain: Nylon 6 Unfilled. I'll be using numbers published by Dow Chemical.
The typical coefficient of linear expansion for nylon 6 unfilled is 8.3x10^-5 mm/mm/'C (An mm of string will expand that many mm per degree change in 'C, or percentage change per temperature.)
Young's Modulus for nylon filament is 5x10^9 N/(m^2)
Since the elasticity is depend upon the cross-sectional area of the string, I will presume the string is 0.70mm wide. Thus, the radius is 0.70/2=0.35mm=0.00035m. The cross sectional area is thus 3.848x10^-7 m^2.
-------- WARNING: BORING ------------------------------------------------
Calculations:
E = FL0/AdL [young's modulus formula]
E = (F/A) / dL% [formula expressed as a percentage change in length]
dL% = (E / (F/A))^-1 [express formula wrt %change in length)
dL% = F/(E*A) [simplify formula]
c = dL%/T [identity of coefficient of linear expansion]
dL% = cT [re-express formula wrt %change in length]
c*T = F/(E*A) [combine two formulas to remove length altogether]
F = E*A*c*T [re-express formula as a function of string tension]
F=E*A*T*c [rearrange formula to make a cool word.. which is no easy...]
[add up the numbers]
F = 5x10^9 N/(m^2) * 3.848x10^-7 m^2 * 8.3x10^-5 (C^-1) * T ('C)
F = T(1924 N * 8.3x10^-5)
F = 0.159692*T (N)
F = 0.16*T (N)
Convert units into ones we use everyday:
0.16 (N) / 9.8 (m/s)/ 1 (kg*m/s) = 0.0163 kg = 0.036 pounds
1 'c *1.8= F
THUS.
One Fahrenheit change in temperature causes a 0.020 pound increase in string tension. Here's a table for your enjoyment:
1 'F = 0.02 lb
1 'C = 0.036 lb
1 'c = 0.0163 kg
1 'F = 0.0091 kg
--------- END CALCULATIONS -------------------------------------------------
What does this mean? The gym I play it gets really cold sometimes (cold enough for me to see my own breath,) which is about a 20'C difference between the temperature at which the racquet at and the temperature of the strings. This means that the tension of my racquet during playtime on cold days is actually 0.72 pounds tighter were I to be using monofilament Nylon strings. That's a small difference you say? Well, we don't use monofilament strings! Since I can't get my hands on actual data, I'll have to do some guesswork.
From the formula, we see that the tension difference is proportional to:
a) Young's modulus
b) Coefficient of linear expansion
c) Cross-sectional area of the string
I'll start with the easy one
C) the tension increasing effect is proportional to the square of the string size. A string twice as thin will increase the tension one-forth times as much. A string four times as thick will increase the tension 16 times as much.
B) Linear expansion is hard to predict. It heavily depends upon molecular structure, and even then, the pattern is not clear. It's why we have material enginners
. I'd say, however, in general, materials more porous and soft will have higher values. Polystyrene has a linear expansion coefficient 60% higher. Acrylic which is hard, has a value 30% lower.
Zyex (used in Ashaway strings) for example has a value TEN times higher than nylon. a string made purely of Zyex would increase in tension by 7.2 pounds in my situation, and probably destroy my racquet. Vectran (used by Yonex) actually has a negative coefficient of thermal expansion, which means it actually EXPANDS when it's cold, and shrinks when it's hot. Since most strings are made out of more than one material, it's very hard to predict the total coefficient. Since most badminton strings feel softer than nylon. I’d guesstimate that the actual value is around 40% higher.
Btw, I suspect Yonex is using vectran partly to limit the effect of temperature on tension, thereby increasing the life of the string and maintaining consistency. Since most materials contract in the cold however, I suspect there is still some shrinkage occurs in Yonex strings overall. Nonetheless this effect would be much smaller, so great work Yonex!
PPS, Vectran is acutally made of carbon-graphite. Neat!
A) Young's Modulus is the ratio of stress over strain. It's kind of like how stiff something is. A string that stretches half as easily would have double the Young's modulus, and hence the temperature effect would be doubled. Since badminton string is usually not as stiff as a nylon string, so one could say this value is actually lower. On the other hand, badminton strings are multifilament strings, which makes the string feel softer without requiring it to be less elastic. This means the softness/bounciness is a matter of string constriction and not as a result of the material properties. Since most strings brag of increased strength, what Young's Modulus actually measures, I'd say the value I used is probably too low. The closest estimate is to use how durable a badminton string is compared to nylon. Since most string manufacturers brag about using materials that strengthen the string, I suspect the real young's modulus of badminton string is 200% higher. This means the temperature effect would be 200% greater than my calculations if we only consider this property. The difference between Young's modulus of nylon and polyester monofilament strings is 400%.
Btw, note that the tension increase felt by the string is determined not just by how much it stretches but also by how much "strength" it can exert per length it stretches. A rubber band can stretch a lot without changing the tension by a large amount, while a steel wire can exert an insane amount of force if it stretched equally as far (about a million greater increase in tension.) Thus, a company that brags that it's strings don't stretch as much during temperature changes is only telling half the story. If it's much stronger, than it could end up hurting your racquet more so than standard strings. Don't believe in marketing eh.
Someone mentioned awhile back that a racquet left in their car trunk was destroyed. I wonder what string it was strung with. Presuming the racquet was strung at 20 pounds in a 25'C/77'F room and left in the car at -20'C/-4'F using typical badminton string, that racquet would have been facing over 45 pounds of tension. No wonder it broke! Btw, since a thermal itself doesn't generate heat, it can only protect your racquet for a brief period before the racquet will be under pressure.
So in conclusion:
Notes: a misplaced bracket gave me a weird result (several million pounds of tension per degree change.) Finding that missing bracket actually took more time than writing this beastly report.
. I haven't been able to find an answer on exactly how much this change is, so I’m going to working out the physics problem here on BF. My physics is a bit rusty so point on any mistakes if you see one. I'm pretty sure I've got everything right though. If you aren't interested in the calculations, just jump to the bottom for the answer. (My feelings won't be hurt... not at all... sniff.)Theory:
When temperature changes, the length of the string changes.
Since the string cannot shrink itself as it is tied at both ends, the net effect it an increase in tension as though the racquet was strung with shorter strings and pulled extra hard to make it fit on the racquet.
Since the effective tension at the point of impact is different from when the racquet is "resting," the effective tension of a racquet in a colder room will be dependent upon the effects of the shift of the "resting" tension. A look from the stress-strain curve of Nylon 6 shows that an increase in stress will cause a greater proportionate percentage change in strain. This means the greater your default tension is, the greater the percentage effect this will have. Hence, racquets strung at high tensions are much much much more vulnerable to this temperature change phenomenon. Since I've never studied engineering, I'll just pull a fast one for this calculation and tell you that this phenomenon doesn't exist
.The numbers:
I wasn't able to find the actual specifications of badminton string, presumably because it is an industry secret, so I’ll be working with the closest polymer that's in the public domain: Nylon 6 Unfilled. I'll be using numbers published by Dow Chemical.
The typical coefficient of linear expansion for nylon 6 unfilled is 8.3x10^-5 mm/mm/'C (An mm of string will expand that many mm per degree change in 'C, or percentage change per temperature.)
Young's Modulus for nylon filament is 5x10^9 N/(m^2)
Since the elasticity is depend upon the cross-sectional area of the string, I will presume the string is 0.70mm wide. Thus, the radius is 0.70/2=0.35mm=0.00035m. The cross sectional area is thus 3.848x10^-7 m^2.
-------- WARNING: BORING ------------------------------------------------
Calculations:
E = FL0/AdL [young's modulus formula]
E = (F/A) / dL% [formula expressed as a percentage change in length]
dL% = (E / (F/A))^-1 [express formula wrt %change in length)
dL% = F/(E*A) [simplify formula]
c = dL%/T [identity of coefficient of linear expansion]
dL% = cT [re-express formula wrt %change in length]
c*T = F/(E*A) [combine two formulas to remove length altogether]
F = E*A*c*T [re-express formula as a function of string tension]
F=E*A*T*c [rearrange formula to make a cool word.. which is no easy...
][add up the numbers]
F = 5x10^9 N/(m^2) * 3.848x10^-7 m^2 * 8.3x10^-5 (C^-1) * T ('C)
F = T(1924 N * 8.3x10^-5)
F = 0.159692*T (N)
F = 0.16*T (N)
Convert units into ones we use everyday:
0.16 (N) / 9.8 (m/s)/ 1 (kg*m/s) = 0.0163 kg = 0.036 pounds
1 'c *1.8= F
THUS.
One Fahrenheit change in temperature causes a 0.020 pound increase in string tension. Here's a table for your enjoyment:
1 'F = 0.02 lb
1 'C = 0.036 lb
1 'c = 0.0163 kg
1 'F = 0.0091 kg
--------- END CALCULATIONS -------------------------------------------------
What does this mean? The gym I play it gets really cold sometimes (cold enough for me to see my own breath,) which is about a 20'C difference between the temperature at which the racquet at and the temperature of the strings. This means that the tension of my racquet during playtime on cold days is actually 0.72 pounds tighter were I to be using monofilament Nylon strings. That's a small difference you say? Well, we don't use monofilament strings! Since I can't get my hands on actual data, I'll have to do some guesswork.
From the formula, we see that the tension difference is proportional to:
a) Young's modulus
b) Coefficient of linear expansion
c) Cross-sectional area of the string
I'll start with the easy one
C) the tension increasing effect is proportional to the square of the string size. A string twice as thin will increase the tension one-forth times as much. A string four times as thick will increase the tension 16 times as much.
B) Linear expansion is hard to predict. It heavily depends upon molecular structure, and even then, the pattern is not clear. It's why we have material enginners
. I'd say, however, in general, materials more porous and soft will have higher values. Polystyrene has a linear expansion coefficient 60% higher. Acrylic which is hard, has a value 30% lower.Zyex (used in Ashaway strings) for example has a value TEN times higher than nylon. a string made purely of Zyex would increase in tension by 7.2 pounds in my situation, and probably destroy my racquet. Vectran (used by Yonex) actually has a negative coefficient of thermal expansion, which means it actually EXPANDS when it's cold, and shrinks when it's hot. Since most strings are made out of more than one material, it's very hard to predict the total coefficient. Since most badminton strings feel softer than nylon. I’d guesstimate that the actual value is around 40% higher.
Btw, I suspect Yonex is using vectran partly to limit the effect of temperature on tension, thereby increasing the life of the string and maintaining consistency. Since most materials contract in the cold however, I suspect there is still some shrinkage occurs in Yonex strings overall. Nonetheless this effect would be much smaller, so great work Yonex
!PPS, Vectran is acutally made of carbon-graphite. Neat!
A) Young's Modulus is the ratio of stress over strain. It's kind of like how stiff something is. A string that stretches half as easily would have double the Young's modulus, and hence the temperature effect would be doubled. Since badminton string is usually not as stiff as a nylon string, so one could say this value is actually lower. On the other hand, badminton strings are multifilament strings, which makes the string feel softer without requiring it to be less elastic. This means the softness/bounciness is a matter of string constriction and not as a result of the material properties. Since most strings brag of increased strength, what Young's Modulus actually measures, I'd say the value I used is probably too low. The closest estimate is to use how durable a badminton string is compared to nylon. Since most string manufacturers brag about using materials that strengthen the string, I suspect the real young's modulus of badminton string is 200% higher. This means the temperature effect would be 200% greater than my calculations if we only consider this property. The difference between Young's modulus of nylon and polyester monofilament strings is 400%.
Btw, note that the tension increase felt by the string is determined not just by how much it stretches but also by how much "strength" it can exert per length it stretches. A rubber band can stretch a lot without changing the tension by a large amount, while a steel wire can exert an insane amount of force if it stretched equally as far (about a million greater increase in tension.) Thus, a company that brags that it's strings don't stretch as much during temperature changes is only telling half the story. If it's much stronger, than it could end up hurting your racquet more so than standard strings. Don't believe in marketing eh.
Someone mentioned awhile back that a racquet left in their car trunk was destroyed. I wonder what string it was strung with. Presuming the racquet was strung at 20 pounds in a 25'C/77'F room and left in the car at -20'C/-4'F using typical badminton string, that racquet would have been facing over 45 pounds of tension. No wonder it broke! Btw, since a thermal itself doesn't generate heat, it can only protect your racquet for a brief period before the racquet will be under pressure.
So in conclusion:
- Thin Vectran-reinforced badminton strings without a titanium core have a very small tension change in temperature changes, probably around 0.3 pounds in 5'C change.
- Thick Zyex-reinforced strings with a titanium core have a large tension change per temperature change, probably around 5 pounds in a 5'C change.
- Since a string manufacturer aren't usually both dumb enough AND unlucky enough to include all the "bad" features, your racquet probably experiences a tension change of around 0.5 pound per 5'C for Yonex strings that use vectran, and 1 pound per 5'C for all other badminton strings.
- Don't leave your racquet outside in the cold if you live a country like Canada, unless you can convince your stringer to do all the stringing outside in the snow
Notes: a misplaced bracket gave me a weird result (several million pounds of tension per degree change.) Finding that missing bracket actually took more time than writing this beastly report.
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