String Tension Formula

Tennis Is Magic · Jul 7, 2011

Okay, I see a lot of threads about people talking about what string tension they should use if their racquet has this string pattern, or this stiffness, and we need to just simplify it here and now.

If using a full bed of a string, use the value for xa in place of ya as well as xa.

(MSS[231]+3)/4 = xa
(XSS[189]+3)/4 = ya

xa or ya * [(NM+NX)/36.5] * (100/RHS) * (65/RA) = xb or yb

If xb>1 or yb>1, 55/xb or 55/yb= recommended tension. If xb<1 or yb<1, 55*xb or 55*yb = recommended tension. If x=1 or y=1, 55 = recommended tension.

Where MSS = main string stiffness, XSS = cross string stiffness, NM = number of mains, NX = number of crosses, RHS = racquet head size (in sq. inches), and RA = stiffness rating.

* For kevlar strings, multiply stiffness by .6

Would put the recommended tension at 61 pounds. Obviously it's not perfect, but I think we can develop it to be more accurate. I'd like you guys to try it and see if it gets you anywhere close to the tension you're using. I know the variables will be skewed for extreme variables. I'll add in a variable for string diameter later after I eat breakfast and make some coffee.

EDIT: RSI String Selector Map 2010 http://www.racquetsportsindustry.com/articles/2010/01/string_selector_2010.html

Up&comer · Jul 7, 2011

I don't know what's more startling to me, this formula or the fact you have 16 posts a day. I don't think I could get the many if I tried.

Anyway, good job. The only problem is that you will need to factor in swingspeed, point of contact, and angle of contact.

Tennis Is Magic · Jul 7, 2011

Up&comer said:
I don't know what's more startling to me, this formula or the fact you have 16 posts a day. I don't think I could get the many if I tried.

Anyway, good job. The only problem is that you will need to factor in swingspeed, point of contact, and angle of contact.

It's easy when half of your posts are reaction pics and posts like this one

TennisCJC · Jul 7, 2011

Tennis Is Magic said:
Okay, I see a lot of threads about people talking about what string tension they should use if their racquet has this string pattern, or this stiffness, and we need to just simplify it here and now.

[MSS(1.1)+XSS(.9)]/180 * [(NM+NX)/36.5] * (RHS/100) * (RA/65) = x

If x>1, 55/x = recommended tension. If x<1, 55*x = recommended tension. If x=1, 55*1 = recommended tension.

Where MSS = main string stiffness, XSS = cross string stiffness, NM = number of mains, NX = number of crosses, RHS = racquet head size (in sq. inches), and RA = stiffness rating.

So if you used Alu Power Rough in the mains, and VS Gut 17 in the crosses in a Babolat Aeropro Drive GT,

[(240[1.1]+82[.9])/2]/180 * [(16+19)/36.5] * (100/100) * (71/65)

This would bring the recommended tension for the string bed to 54 pounds. Now if you move the gut to the mains, and poly to the crosses,

(82[1.1]+240[.9])/180 * [(16+19)/36.5] * (100/100) * (71/65)

* All variables including kevlar = 300.

Would put the recommended tension at 61 pounds. Obviously it's not perfect, but I think we can develop it to be more accurate. I'd like you guys to try it and see if it gets you anywhere close to the tension you're using. I know the variables will be skewed for extreme variables. I'll add in a variable for string diameter later after I eat breakfast and make some coffee.

The formulas are too complex for me but I do know this formula:

Poly string at 61 lbs = tennis elbow and sore wrist

I would not recommend for anyone to play poly strings at these tensions. I would say keep you poly tensions between 40-52 lbs on all frames.

Tennis Is Magic · Jul 7, 2011

TennisCJC said:
The formulas are too complex for me but I do know this formula:

Poly string at 61 lbs = tennis elbow and sore wrist

I would not recommend for anyone to play poly strings at these tensions. I would say keep you poly tensions between 40-52 lbs on all frames.

Not necessarily, I play a full bed of first gen poly in a 71 RA racquet at 60 and it feels like butter

The formula is complex, but it DOES account for some of the major factors in choosing string tension which is the stiffness of the string, the string pattern, the headsize, and the stiffness, and I think it's a more objective way to choose a starting tension, as opposed to subjective opinions such as "Gamma Monoblast in a Dunlop 4D 500 Tour at 60 pounds was one of the best string jobs I've ever used, it's awesome try it!" Most users here would flame me from now until eternity for posting that, but that's my opinion. Opinions are useful, but at some point, they're limited by the experiences people have used to develop them.

zcarzach · Jul 7, 2011

Interesting idea. Where did you get the numbers for the main and cross string stiffness? Is this an easily accessed piece of information?

Tennis Is Magic · Jul 7, 2011

zcarzach said:
Interesting idea. Where did you get the numbers for the main and cross string stiffness? Is this an easily accessed piece of information?

Yes, I got those from RSI's website. I'll add that to the OP right now, since you reminded me

Power Player · Jul 7, 2011

Ok, I suck at math. Here are the variables for someone to run through.

Main 17 gauge Genesis Black Magic
Cross 16 Gauge Gosen OG Sheep Micro
Racquet - 100 square inches
Stiffness - 66 RA

Pattern - 16x20

zcarzach · Jul 7, 2011

Tennis Is Magic said:
Yes, I got those from RSI's website. I'll add that to the OP right now, since you reminded me

Thanks for clarifying. When I run the numbers for my nCode Tour 90 with Gosen OG 18 mains and Gosen Polylon 17 crosses, I get 52.17, which is quite close to the 53 / 51 tension I have been using. So, nice job!

zcarzach · Jul 7, 2011

Power Player said:
Ok, I suck at math. Here are the variables for someone to run through.

Main 17 gauge Genesis Black Magic
Cross 16 Gauge Gosen OG Sheep Micro
Racquet - 100 square inches
Stiffness - 66 RA

You are missing the number of mains and crosses from this.

zcarzach · Jul 7, 2011

Actually, you don't have to take into account the string diameter. The RSI chart takes string gauge into account! I'm still impressed with the formula, by the way, since it was so close to my preferred setup.

Power Player · Jul 7, 2011

zcarzach said:
You are missing the number of mains and crosses from this.

Ok thanks..edited.

Tennis Is Magic · Jul 7, 2011

Power Player said:
Ok, I suck at math. Here are the variables for someone to run through.

Main 17 gauge Genesis Black Magic
Cross 16 Gauge Gosen OG Sheep Micro
Racquet - 100 square inches
Stiffness - 66 RA

Pattern - 16x20

Tennis Is Magic's String Tension Formula™ recommends an initial tension of 43 pounds.

Power Player · Jul 7, 2011

Hmm..that would not work for me. I am stringing this setup at 58#s and it is about perfect. Shots dropping right inside the baseline.

43#s with a synth gut in the cross is not going to work ..maybe this formula is better suited for full jobs?

Tennis Is Magic · Jul 7, 2011

Power Player said:
Hmm..that would not work for me. I am stringing this setup at 58#s and it is about perfect. Shots dropping right inside the baseline.

43#s with a synth gut in the cross is not going to work ..maybe this formula is better suited for full jobs?

Well, like I said, string setup is subjective, so it won't ALWAYS hit the mark. I did try to mold it in the likeness of what frequenters here tend to prefer, but there are always outliers. I think I need to adjust the string stiffness denominator so string stiffness isn't as large a factor in determining the final value. If you exclude string stiffness, the final value of your recommendation would have been 55.

Power Player · Jul 7, 2011

Yeah, thats a lot better..55 would work.

aggielaw · Jul 7, 2011

Seems to be a consistently low result.

I have the following setup (relevant values in parens):
Yonex RQiS Tour 1 XL (95 head size)(64 stiffness)(16x19 stringbed)
Babolat Tonic + Ball Feel (114 stiffness from cited RSI article)

That gets me to: x=[114(1.1)+114(.9)]/180*[(16+19)/36.5]*(95/100)*(64/65), which according to myalgebra dot com equals 1.136, which then becomes 55/1.136, which equals 48.4 recommended tension. If I take the tension multipliers out (1.1 and .9) the formula comes out the same.

Man, I can just imagine the trampoline my racquet would become with that setup! :shock:

Tennis Is Magic · Jul 7, 2011

aggielaw said:
Seems to be a consistently low result.

I have the following setup (relevant values in parens):
Yonex RQiS Tour 1 XL (95 head size)(64 stiffness)(16x19 stringbed)
Babolat Tonic + Ball Feel (114 stiffness from cited RSI article)

That gets me to: x=[114(1.1)+114(.9)]/180*[(16+19)/36.5]*(95/100)*(64/65), which according to myalgebra dot com equals 1.136, which then becomes 55/1.136, which equals 48.4 recommended tension. If I take the tension multipliers out (1.1 and .9) the formula comes out the same.

Man, I can just imagine the trampoline my racquet would become with that setup! :shock:

The multipliers are meant to adjust the values for hybrids. Using them when the stiffness values of the mains and crosses are different cause the final value to increase or decrease because the mains and crosses affect the overall string job disproportionately. If you're using a full bed of a string, you will get the same value if you take out the multipliers.

And yes, I can see the average string stiffness value is too low. Value changed to the initial value of 200. Also imposed new limits on kevlar, poly, and gut strings to reduce the enormous effect string bed stiffness has on the values.

Jonny S&V · Jul 7, 2011

Wow, this thread made me cry a little. Isn't a formula like this a little unnecessary?

Tennis Is Magic · Jul 7, 2011

Jonny S&V said:
Wow, this thread made me cry a little. Isn't a formula like this a little unnecessary?

It is, but maybe this will cut down some of the excessive "what tension should I use" threads that pop up a dozen times a day.

Jonny S&V · Jul 7, 2011

Tennis Is Magic said:
It is, but maybe this will cut down some of the excessive "what tension should I use" threads that pop up a dozen times a day.

If it did, cool, but it won't... :-(

Power Player · Jul 7, 2011

Exactly..it won't because there is no formula for personal choice. People just need general guidelines to start with and I do not believe the formula provides it.

Tennis Is Magic · Jul 7, 2011

Power Player said:
Exactly..it won't because there is no formula for personal choice. People just need general guidelines to start with and I do not believe the formula provides it.

Well, it could if we tweak it. String stiffness is so hard to quantify because of the wide range of stiffness. There are strings under 100 and strings over 900. Maximums and minimums should help, though I'd rather find a multiplier to make a more accurate variable than limits.

EDIT: More tweaks added to the formula. I've added multipliers and dividends to limit the high end and low end stiffness ratings, yet hold their values relative to other strings.
EDIT: THERE, I've found about as happy a balance as I can find between the low extreme of natural gut, and the high extreme of poly and kevlar. This should be more realistic.

itsEr · Jul 7, 2011

Tennis Is Magic said:
It is, but maybe this will cut down some of the excessive "what tension should I use" threads that pop up a dozen times a day.

I agree, it'll lessen the new threads, but you might end up doing the math for them.... Anyway, I like the formula, it worked for me, thank you for it

fortun8son · Jul 7, 2011

Stringing is as much an Art/Craft as it is a Science.
If you're willing to do the math, the formula can give a reference point.
Here's an easier formula:
For Nylon or Natty, start at the mfg suggested middle.
For poly, start 10% lower.
For Kevlar, start 20% lower
OK, It's summer. You can start 2-3lbs higher.

Tennis Is Magic · Jul 8, 2011

fortun8son said:
Stringing is as much an Art/Craft as it is a Science.
If you're willing to do the math, the formula can give a reference point.
Here's an easier formula:
For Nylon or Natty, start at the mfg suggested middle.
For poly, start 10% lower.
For Kevlar, start 20% lower
OK, It's summer. You can start 2-3lbs higher.

That's what the formula does, it basically accounts for all the perceived notions we hold (eg. string nat gut higher, poly lower, string higher for stiff racquets and lower for flexible racquets, etc.)

SStrikerR · Jul 8, 2011

Hmm, be nice if someone could make a program/calculator where people could input the variables (string, string pattern, etc) and it would calculate it for you. Tools like that are always helpful, especially if the formula is refined a bit and works better.

But while I'm at it:

RHS- 95
RA- 67
MSS- 240
XSS- 240
NM- 18
XM- 20

The string is all poly, if it matters.

Tennis Is Magic · Jul 8, 2011

SStrikerR said:
Hmm, be nice if someone could make a program/calculator where people could input the variables (string, string pattern, etc) and it would calculate it for you. Tools like that are always helpful, especially if the formula is refined a bit and works better.

But while I'm at it:

RHS- 95
RA- 67
MSS- 240
XSS- 240
NM- 18
XM- 20

The string is all poly, if it matters.

Recommended tension is 50 lbs.

TimothyO · Jul 8, 2011

Far more useful than this calculator is a DB of favored frames and string configurations.

I did something like that using Colin the Stringer's information. As Gomer Pyle might say, "Surprise, surprise, there's a pattern!". If you arrange the players by string type (eg gut/poly hybrids) and frame characteristics then patterns for tensions emerge. There are ranges of values with some outliers but there are also clusters.

This makes sense since the community exchanges information, the laws of physics are the same for everyone, but everyone is a little different in physique, skill, and personal prefence.

Such a DB, searchable by stringing category and sortable by frame characteristics would be very helpful. Sort of like a Stringing Wiki to which anyone could contribute.

SStrikerR · Jul 8, 2011

Tennis Is Magic said:
Recommended tension is 50 lbs.

Nice, my setup is at 49lbs, but that was just a guess after finding 55 to be too high.

Tennis Is Magic · Jul 11, 2011

SStrikerR said:
Nice, my setup is at 49lbs, but that was just a guess after finding 55 to be too high.

Yes, I think I've FINALLY perfected it

jstout · Jul 11, 2011

Pro Staff 6.1 Classic with my two string setups. My normal is 61 lbs for the Synthetic and 56/60 for the Hybrid.

RHS- 95
RA- 72
NM- 16
XM- 18
MSS- 204 (Synthetic) or 242 (Poly)
XSS- 204 (Synthetic) or 200 (Synthetic)

My Synthetic setup comes out to 51 lbs and my Hybrid comes out to 49 lbs.

Seems low since all Synthetic should likely be higher tension. Also seems the string is making little difference in the formula.

Tennis Is Magic · Jul 11, 2011

jstout said:
Pro Staff 6.1 Classic with my two string setups. My normal is 61 lbs for the Synthetic and 56/60 for the Hybrid.

RHS- 95
RA- 72
NM- 16
XM- 18
MSS- 204 (Synthetic) or 242 (Poly)
XSS- 204 (Synthetic) or 200 (Synthetic)

My Synthetic setup comes out to 51 lbs and my Hybrid comes out to 49 lbs.

Seems low since all Synthetic should likely be higher tension. Also seems the string is making little difference in the formula.

String does make a difference in the formula, to the point that polys were regularly registering in the 40s and gut was upwards of 70 the first time. I nerfed the difference. I'll run the numbers on this, but your racquet looks like it would register a much higher number due to the stiffness.

Found one small glitch in the formula, I forgot to adjust it so it finds an average between stiffness of mains and crosses combined, this is making the results significantly lower than intended. Real result should be 61.35348728350757, or 61 lbs for your hybrid, and 60.22080751827358 full poly. Apparently I have to reduce the multipliers even further to create more distinction between strings.

zcarzach · Jul 11, 2011

Post deleted.

Tennis Is Magic · Jul 11, 2011

zcarzach said:
Running your scenario through the Excel doc I made, then edited according TiM's updates, I get 58.4 for your all synthetic setup and 59.6 with the poly mains and synthetic crosses.

That has to be backwards, string stiffness decreases the recommended tension. All things equal, tension should be down about 2 pounds.

Recommended tension is 62/63 full synthetic, 61 for poly/syn hybrid. Also, note the formula does not recommend tension differences in the strings. I can modify it so that it does, but that will have to wait until later, as I have things to do today.

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