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Calvin's Corner

More on keeping things in balance

The previous Calvin's Corner article reviewed the Tension Conversion Calculator, an Excel spreadsheet for the TM-1. This spreadsheet provides a graphic aid to understanding and seeing spoke tension relationships in the wheel. This article will provide more details and instructions on how to balance the tension. To fully understand this article, it is necessary to be familiar with the TM-1.  The article uses "radar" charts that visually show the tension relationship between the 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 to end up tighter relative to other spokes, and yet for the wheel to spin straight and true. These spoke tension imbalances can usually be corrected. However, there may be some imperfections in the manufacturing of the rim which will simply not all exactly equal tension between spokes.

Wheel example #1 below is a rear 32-hole rim. The wheel originally had 36 kgf average on the right side, which would be considered very low overall tension (figure 1). The wheel was also badly out of round and lateral true.

Figure 1. 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 1 to figure 2. This is because lateral and out-of-round errors were corrected.

Figure 2. The run out (wobble) is corrected and the wheel spins straight and round with somewhat higher overall 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 3). The right side tension increased to 67 kgf, and the left side increased to 43 kgf. Now the centering (dish) of the rim 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 3. 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 a 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 4). 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 4. 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 4 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 5 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 5. 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 6). 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 6. 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 7). The wheel is now ready for use.

Figure 7. 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 8). 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 4 , 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 8. 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 9, 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 10). However, in another experiment, a box section carbon tubular rim showed no measurable drop with high pressure.

Figure 9. 121 kgf before tire was mounted and inflated

Figure 10. 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 of a 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 13). The star shaped pattern is a result of the "pulling" and "pushing" spokes increasing or decreasing in tension under load.


Figure 13. 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 damaged 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 riding throuhg 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 14). 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 14. 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 15). 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 16).

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 15. A common flange spacing for rear road hubs


Figure 16. 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 17). This will increase the left side tension relative to the right side (figure 18).

Figure 17. A rotor front hub with asymmetrical left and right flanges

Figure 18. 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 19 illustrates broken right side spoke at #8, now at 0 kgf. This wheel was originally well balanced (figure 7).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 19. 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 20). 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 20. 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 21, the rim was popped back. Notice the two similar left and right side patterns, but each offset slightly.

Figure 21. "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 22).

Figure 22. 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.