TCC: Tension Conversion Calculator for TM-1
Note: This page is a re-introduction of the Tension Conversion Calculator (TCC). To appreciate the TCC, you should first become familiar with the TM-1.
The TM-1 uses a tension conversion table that lists conversions from the tool deflection reading into kilograms force, or the amount of pulling force on the spoke. Tensiometers work by pushing against the spoke and taking a reading of the amount of "push" or deflection. The TM-1 has a chart that converts the tool reading (a "deflection reading") into the amount of force pulling on that particular spoke. The TM-1 can measure the spoke tension (force) pulling on the rim. It can also be used to determine if the spokes are relatively even in tension between one another.
On a computer with Windows® Excel or an equivalent program installed, the TCC uses information drawn from the tension conversion table in a spreadsheet. The TCC greatly speeds converting a deflection reading from the TM-1 into a measure of tension force on the spoke. Additionally, the TCC creates a visual representation showing the tension balance between the spokes of the wheel. The TCC also allows the professional builder and mechanic to document on paper the quality of their work, and other wheels can be evaluated for tension problems.
NOTE: The TCC is provided as a support service for the TM-1. It will not work with other tension meters other than the Park Tool TM-1. Park Tool will appreciate any feedback, questions, or comments. Please email info@parktool.com directly any concerns. Use subject line "TCC".
There are two different version of the TCC spreadsheet. The TCC_15.xls works with Windows® operating systems. This version uses "VBA" and will not work with many MAC's. PC users should download and save the file below. Both version will produce similar results and yield a chart similar to the one below (figure 1):
Figure 1. Example of TCC spreadsheet
TCC_Revision15FormBased.xls (PC USERS ONLY)
After downloading the file to your hard drive, open the file. The spreadsheet software will ask you to "enable macros". The macros must be enabled for the TCC to work. This version of the TCC uses one file, with one worksheet called "Instructions". As you create new charts, the finished worksheet will open as a tab. Data is entered on a series of forms. The first form begins with creating a name for the Sheet. This can be a short description of the wheel, or the customers name.
After filling in the Sheet Name, click the box below, "Set Up Sheet for this Wheel". After this, click the box, "Next". The next form begins with Select Spoke Type. View first spoke material, shape and size. Do not use the ordered number of spoke as the spoke size. A 2mm spoke is the forth spoke down, "steel, round 2". Highlight the correct spoke, then enter the right and left side spoke counts. Typically these are the same. You must also list a target tension. If you are not sure, enter 100.
The form for data entry will open. Enter the reading from the TM-1 here. You will see the Kilogram force converted as you proceed. This page also averages the wheel kgf values. Any spokes that are outside of a plus or minus 20% range are highlighted in red. This can be useful when tension balancing the wheel. After entering the right side data, click NEXT and repeat for the left side. Click FINISH and the chart will appear. This page will not accept new data changes after hitting FINISH. All readings and kgf values are listed here, and a graphic representation of the wheel is shown. The left side and right sides are shown seperately, and then a combined chart showing the two side together.
ERRORS
This project and spreadsheet are a working version. You may experience errors, sometimes seen at a "Run Time Error". If this occurs, cancel and close the form and then delete that worksheet form the file. Begin a new worksheet.
MAC with 2008 Microsoft Office
The MAC using the 2008 Microsoft office is unsupported at this time. A separate TCC is to follow.
TCC_13MAC.xls for MAC users
After downloading the file to your hard drive, open the file. The spreadsheet software will ask you to "enable macros". The macros must be enabled for the TCC to work. Begin by selecting the page titled Spoke Tension Record. You may need to change view if you cannot see the entire spread sheet. Select "Zoom" from "VIEW" in the tools menu. Next, select the page titled Instructions.
You will need to use and be familiar with the Windows® Excel program to open and run the TCC. The program will ask you to "Enable Macros". Macros must be enabled for the TCC to operate. It is recommended that you save the file when you download it with the original file name as given. As you work on new wheels, you can perform a "save as" procedure and rename the file for the wheel being worked on. The file name can include the date of service, customer, or model of wheel. Unlike the PC version of the TCC, the TCC_13MAC.xls uses one file per wheel.
There will be two worksheets in in the TCC, which are labeled on the bottom as Instruction and Spoke Tension Record. Begin by reading the Instruction page before continuing with the Spoke Tension Record.
The TCC has room to record consumer or user information such as name, address, etc. There is also room to record wheel information such as rim, or hub cross pattern. The key buttons are the MACRO CONTROLS. Begin by clicking "Step 1, Spreadsheet reset " to clear the sheet. For the next step, notice first the SPOKE CODE TABLE. You will see a code number next to descriptions of various spoke types. There are more choices on this TABLE than on the paper chart included with the TM-1. Find your spoke type, and click on "Step 2 Spoke Code". Enter the code here. Do not attempt to enter the spoke size or dimensions, only the SPOKE CODE.
The next step is Step 3. Click the MACRO CONTROL, "Step 3, Right Side Spoke Count". This is commonly one-half the number of spokes in the wheel. If there are 32 holes, enter here 16. Notice the diagram change to show the chart having your selected spoke configuration.
Step 4 is optional, but useful. Click the MACRO CONTROL "Step 4, Target Spoke Tension" and enter the desired kgf average. The TCC will give you the TM-1 reading equal to that kgf.
After these steps, make sure the cursor is in the RIGHT SIDE SPOKES table, in the "TM-1 Reading" box next to "Spoke Number 1". It is recommended to begin at the valve hole. On the right side of the wheel, number the spokes to the right from here (figure 2). On the left side of the wheel, work from the valve hole again, but number the spokes to the left. This system will keep the numbers of the left and right side spokes adjacent to one another on the chart.
Figure 2. The TM-1 is measuring spoke #5, as seen written directly on the rim braking surface
As you enter TM-1 reading, you will see the TCC convert these to Spoke Tension. The TCC will automatically determine the Average Spoke Tension ( in kgf), the standard deviation in tension, and the tension limits and reading limits in a range of plus and minus 20% of your average. Wheel builders may decide that they want a tighter range than this default 20%. For example, if you want a plus or minus 10% range, multiply your average by 1.10 and then by 0.9 for your kgf averages. The graphic chart to the right of the RIGHT SIDE SPOKE table shows visually the relationship between the spokes. Record readings from the left side of the wheel under the table LEFT SIDE SPOKES. The average tension in Kilograms Force (kgf) is again determined.
Notice the chart "Combined Spoke Tension". This is a graphic representation of forces between the left and right side spokes. This can be used to correct tension imbalances and for diagnosing potential problems with the wheel.
Tension Balance with the TCC
The TCC Spreadsheet is a tool to help the wheel builder achieve a good average spoke tension. It can also speed the process of "tension balancing. This adjsuting the spokes so they are relatively the same tension. Spokes that are too tight or too loose relative to other spokes create problems. However, it is unlikely all the spokes are exactly the same tension. There may be some imperfections in the manufacturing of the rim which will simply not all exactly equal tension between spokes.
A wheel built with spokes that are close to the same tightness, that is “tension balanced”, will produce a wheel that stays true longer. The spokes will also be more resistant to "stress cycles", a tightening-loosening effect that leads eventually to spokes breaking.
As spokes are tightened and adjusted when truing a wheel some spokes are worked more than others. Each spoke pulls on a section of rim, moving it left-to-right laterally, and also toward or away from the hub radially. However, spokes also control an area of the wheel wider than the point where they attach to the rim. When a wheel is pulled tight, it is common for some spokes end up tighter relative to other spokes, and yet for the wheel to spin straight and true. These spoke tension imbalances can be usually be corrected.
Wheel example #1 below is a rear 32-hole rim. The wheel originally had 36 kgf average on the right side, which would be consider very low overall tension (figure 3). The wheel was also badly out of round and lateral true.
Figure 3. Rear wheel with both low tension and poor true
The lateral and round errors in example wheel #1 were then corrected. This increased the right side tension average of 46 kgf, and the left side to 34 kgf (figure 2). This left-to-right tension difference is normal on wheels with offset, or “dish”, such as multiple geared rear wheels, or front wheels with a rotor braking disc. Notice also the change in spoke tension pattern of the graphic chart from figure 3 to figure 4. This is because lateral errors in lateral and out-of-round errors were corrected.
Figure 4. The run out (wobble) is corrected and the wheel spins straight and round with somewhat higher overal all tension
The wheel now spins straight and round, however, the wheel still needs more overall spoke tension. An additional turn is added to each nipple and then the wheel is double checked for good lateral true, and tension measured again (figure 5). The right side tension increasesd to 67 kgf, and the left side increasesd to 43 kgf. Now tThe centering (dish) of the rim was is off, and must be corrected, which again will add more tension. Although the overall tension is increasing, notice the relative tension patterns remain as before. The left side (blue) appears to be the head of a cat, with two pointed ears.
Figure 5. Increases in tension tend to maintain the same spoke-to-spoke tension patterns
More tension is added by tightening the nipples further, and the wheel is now fully true. Lateral run out, round (radial trueness) and centering (dish) all well within tolerance of 0.5mm. The right side tension average is 125 kgf, and the left side average is 66 kgf. However, while the average right side tension is within the rim manufacturers recommendations, the spokes on the right range from as low as 95 kgf to as high as 156 kgf (figure 6). This wheel could be sent out to the customer, but it could be made better. By balancing the right side spoke to one another, and then balancing the left side spokes to themselves, the wheel will be less likely to come out of true.
Figure 6. Fully tight and straight wheel but with poor spoke tension balance
In this example, the right side tension varies substantially. Right side spoke #1 is relatively low in tension. Note that this tight spoke is next to right side #16, which is relatively tight. By loosening #16, it will drop in tension, but the wheel will also move laterally to the left. Right side spoke #1 must then be tightened to both increase tension and to bring this section of the wheel back into lateral true. It is common in a wheel to see same-side tight spokes adjacent to a relatively loose spoke. In figure notice right side #13 is next to a loose #12.
In viewing the blue graph (left side), left side spoke #2 is next to a loose left side #1, and also adjacent to loose left side #3. It may be possible here to spread the extra tension of left #2 to both left #1 and left #3.
When making minor tension balance corrections, begin with 1/4 turn. If the relative spoke tension is extreme (over 20%) attempt to correct it with 1/2 turn. Figure 7 is the wheel shown in the chart of figure 4. Right spoke #3 can be balanced against right side #4. Right side #16 can be balanced to spoke #1. Spoke #15 is at the average already. Spoke #2 is a little low, and there is no right side adjacent spoke to balance it. It can happen there is no immediate spoke to partner with for balancing. However, this spoke is not as badly imbalanced as the others, and it is simply left alone for now.
NOTE: Right side spokes balanced to other right side spokes. Left side spokes balanced to one another. Left side spokes and rights side spokes will not be the same tension on this wheel.
Figure 7. Overly-tight right side spokes are matched to other low-tension right side spokes to achieve good tension balance
The result is a well-balanced wheel (figure 8). The same procedure as above is repeated on the left side, again, matching only left side spokes to other left side spokes. Notice also the "cat" image on the left is now gone. The concept of tension balancing is to maintain acceptable run out (trueness) while balancing out the spoke tension (left side to left, right side to right). Although the example wheel is not "perfect" it is much better and is within plus or minus 10% of the average for all spokes; again, left side compared to left, and right side compared to right.
Figure 8. Example #1 wheel after tension balancing spokes
The last procedure for the wheel is "stress-relieving". This causes the spokes to pop and ping, which relieves any wind-up they may have. This procedure also tends to help the tension balance (figure 9). The wheel is now ready for use.
Figure 9. Example wheel after pre-stressing the spokes
Radial Stress
The rim of the wheels tends to flatten slightly when loaded vertically. This is normal and occurs during riding. The bottom spokes will drop slightly in tension (figure 10). The spokes at 90-degrees from the bottom, at the 3:00 and 9:00 positions, rise in tension. The spokes at the 12:00 or straight up position do not gain tension. Every time the wheel rotates, each spoke goes through this cycle of getting looser and tighter. With enough use, the spokes will see millions of stress cycles, and this may cause them to fail by breaking.
This loosening effect of simply riding is an example of why balancing is useful for the wheel. If the example wheel were used as shown in figure 5 , the low spokes would drop even further in tension when ridden, and this would tend to loosen the nipple. Like all fasteners, the tendency is that a loose bolt and nut will get even looser during use.
Figure 10. Rear wheel under radial load
Air Pressure Effect of Tension
When the tire is inflated, it effectively squeezes the rim. This has the effect of dropping slightly the overall spoke tension. Not all rims will respond in the same manner. In figure 11, a light road rim was balanced and set at 121 kgf for the right side. After inflating the tire to 125 psi (8.5 atms) the tension dropped to 105 kgf (figure 12). However, in another experiment, a box section carbon tubular rim showed no measurable drop with high pressure.
Figure 11. 121 kgf before tire was mounted and inflated
Figure 12. Same wheel as figure 9 is now 105 kgf after tire inflated to 8.5 atms
NOTE: Do not add additional tension in anticipation of the effect of tire pressue. The effect is already figured in by the manufacturers recommendations. Consult rim manufacturers for most current tension recommendations.
Torsion (twisting) Applied at Hub
When the cyclist pedals, the chain pulls on the rear cogs, which rotates the rear hub, and eventually rotates the wheel and tire (figure 11). This twisting or rotational force is transmitted through the spokes. For hubs that have a tangent lacing pattern the tension will change when this torsional force is applied (figure 12). Spokes radiating to the back are called "trailing" or "pulling spokes". Spokes radiating forward are "leading" or "pushing spokes".
Figure 11. Rear hub applying a twisting or torsional load to wheel
Figure 12. Common tangent lacing showing "pulling" and "pushing" spokes the rear hub
A similar torsion or twisting load is applied through the spokes by rotor disc braking. Rim caliper brakes do not apply braking force through the spokes in the same way. The load and stress on the rotor hub and spokes can be much greater from braking compared to pedaling (figure 15). The star shaped pattern is a result of the "pulling" and "pushing" spokes increasing or decreasing in tension under load.
Figure 15. Extreme effect of twisting hub from rotor brake use
Lateral Stress- normal use and non-destructive loads
It is normal and common for a rim to see some lateral stress and not become permanently damage or deformed. In figure 14, a fully tensioned and balanced rear wheel rim was pulled laterally to the right, moving the rim over 10mm at spoke #2. This would be similar to be in a corner while going over bumpy terrain. In this example, the left side spokes in the area of #2 increase in tension, and the right side spokes drop in tension (figure 16). However, notice the "egg" or ovalizing effect on tension. The right side flattens, but the left side flattens 90-degress from the orientation of the right side. This rim returned to normal true after release of the lateral stress. This is an example of the importance of not setting tension too high. If spokes are set to an extreme tightness, the forces might exceed the yield strengths of the spokes and rim. This shows that normal riding increases tension at the point of stress. If this were an unbalanced wheel, with widely varying tension, extreme stress on the over-tight area might result in a cracked rim.
Figure 16. Non-destructive lateral loading of rear wheel. Wheel returned to normal trueness after stress removed.
Dish or Centering
The rim is typically centered to the hub as measured between the axle locknuts. This places the rim in the center of the rear frame or front fork. If the flanges of the hub are symmetrical and centered to the locknuts, the left and right side tensions tend to be equal. However, on rear wheels with multiple gearing, or on front hubs with a rotor disc, the flanges are offset to the hub locknuts (figure 17). A typical rear road hub is 130mm wide, but the left flange may be 36mm from the hub center, while the right flange may be 17mm. However, designs vary slightly between manufacturers (figure 18).
If the left-to-right tensions are compared on these road hubs, the left side will be approximately 55% of the tighter right side. For example, if the right side tension is 100 kgf, the left side may be approximately 55 kgf. As rear hubs widen, the left to right flange spacing narrows, and the left to right tension differences decrease.
NOTE: Rim manufacturer's tension recommendations are for the tight side of any wheel. The non-tight side is set simply by having correct dish (centering) when the tight side is at the recommended tension.
Figure 17. A common flange spacing for rear road hubs
Figure 18. Two different road wheels with different flange spacing
Front hubs that use a rotor disc will also have a tight side and a looser side. The rotor side flange will be closer to the hub center (figure 19). This will increase the left side tension relative to the right side (figure 20).
Figure 19. A rotor front hub with asymmetrical left and right flanges
Figure 20. Tension relation of a common rotor front wheel
Broken Spoke
Spokes can with use and time can eventually fail and break. When one spoke fails it will affect the entire wheel to some degree. The area of rim at the spoke failure will come out of true. This section of rim will move laterally. Figure 21 illustrates broken right side spoke at #8, now at 0 kgf. This wheel was originally well balanced (figure 9).The two neighboring spokes, right side #9 and right side #7, went up in tension because there was no longer pulling at right side #8. However, the entire right side tension has changed, showing an ovaling of the pattern, with tension increasing opposite the breakage. Corresponding to this effect is the ovalizing of the left side, but again at a 90-degree offset. The left spoke right at the area of right side #8 rose in tension because the rim is also now pulling away from the hub. The wheel pulls to the left at the area of spoke #8, but also pulls to the right at right spoke #16, which have increase in tension as a result of the broke #8. .
Figure 21. Wheel tension from broken spoke #8 on the right side
Lateral Impact
If the rim has experienced a major lateral impact, it may fold or "taco". This is an interesting phenomenon in tension. There is a similar pattern on each side, but offset by 90-degress (figure 22). Right side spokes #2, #3. #4, and then #11, #12, and #13 are tight. However, away from these spokes the tension quickly falls off, with spokes #6, #7, #8, #9, and then #15, #16, and #17 effectively 0 kgf. The pattern repeats on the left side, but here the tight spokes are #16, #17, #18, and then #7, #8 and #9.
Figure 22. The folded or "taco" rim pattern, not a "lucky four-leaf clover" for the rider
It is claimed by some that this "taco" can be fixed by re-bending the wheel. This can be done to some degree, but also leads to unusual spoke tension issues. In figure 23, the rim was popped back. Notice the two similar left and right side patterns, but each offset slightly.
Figure 23. "Taco'd" rim was struck to "fix" the bend
The rim re-bent rim was approximately 7mm out of lateral true, which would be unacceptable for use. Spoke tension was used to correct the wheel to approximately 1mm lateral error (figure 24).
Figure 24. Bent lateral rim straightened with spoke tension correction. It may leave the shop, but will not hold up well under use.
Special Thanks
The Park Tool Company would like to thank Julie Howat and Colin S. Howat of Howatrisk.com, Lawrence, Kansas, for the assistance and help in developing the TM-1 and for the development of TCC.
