From a theoretical perspective, the choice to use carbon fiber over aluminum is well founded. The stiffness of a material is quantified by a metric called Young’s modulus. On that wikipedia page, the stiffness for carbon fiber is listed at 181 GPa while that of aluminum is 69 GPa. Thus, a carbon tripod with the same tube dimensions as an aluminum will perform much better. In addition, the carbon fiber is less dense than aluminum and will therefore the tripod will be lighter as well.

This simplistic comparison is far from the whole story. In practice, carbon fiber tubes vary wildly in quality and stiffness. There are many factors that go into making a carbon fiber tube such as the direction of the fibers, the modulus of the fibers, and the resin/fiber ratio. For example, that same wikipedia page referenced in the above paragraph lists a different carbon fiber as having a modulus of 30-50 GPa, far less than aluminum. It is easy to save cost on the manufacturing side by having by using poor quality tubes while still being able to market the tripod as carbon fiber. Tripod manufacturers often list the number of layers of carbon fiber used in their tubes, but this to can be misleading and only has a small correlation with the final tube stiffness. There is a reason that none of the top manufacturers list the number of layers in their tubes. Its a meaningless measure. I know of no way to glean the quality of the carbon fiber tubes used in a tripod short of measuring the tripod stiffness as done on this site. There is vastly more to say regarding carbon fiber, such as the non-isotropic nature of the stiffness, and I likely will in a future post. For now, let us simply note that there is a huge variance in the stiffness of different carbon fiber composites.

Below is a plot of the height adjusted stiffness versus weight for every tripod I have tested. This is simply a visual representation of the rankings page. The further up and to the left a tripod is on the plot, the better the score. In this plot though, the aluminum leg tripods are plotted in blue, and those with carbon fiber legs are plotted in red.

The difference in performance is clearly apparent, with carbon fiber tripods performing much better than the aluminum ones. What is particularly interesting is that the aluminum tripods all appear to fall on a line, with the stiffness being roughly proportional to the weight. It appears that the old notion that stable tripods are necessarily heavy is correct when it comes to aluminum legs. For carbon fiber legs, we see a lot more dispersion between the lowest and highest performing tripods at a given weight. This makes perfect sense given our understanding of the wide range in the quality of carbon fiber tubing. The best carbon fiber tripods are dramatically lighter and stiffer than an aluminum one. The worst ones appear to have similar stiffness to an aluminum counterpart while still maintaining weight advantages.

Theoretically, carbon fiber also appears to have better damping than aluminum. Data for the damping ratio can be found for both aluminum and carbon fiber composite. The damping ratios for are better for the carbon fiber composites than for aluminum by a factor of between 1-3x depending on the sample of carbon fiber used and direction of vibration. Damping ratio depends on the stiffness and weight of the material. Carbon fiber is generally stiffer and lighter, and these would roughly offset each other in magnitude so the damping ratios should be somewhat comparable. Just be warned that we are doing some serious back of the envelope science here. Note that the damping figures reported on this site are not a ratio, but the absolute damping coefficient and are directly comparable to each other. Again, carbon fiber composite can be manufactured in many different ways, and we should naturally expect variance in the damping properties. In summary, we should expect better damping properties from carbon fiber legs.

With some expectations under our belt we can now take a look at the data. Below is a plot of the mean damping (harmonic mean of pitch and yaw damping) versus the tripod weight. The logic of this plot is less theoretically sound than that of the stiffness one, but is still useful.

The carbon fiber tripods still appear to do better on average, but not dominantly so. As we have seen in previous posts, damping can behave in funny ways compared to the nice linear behavior of stiffness. In particular, it is easy to add a lot of damping to a tripod simply by varying the material of the top plate or engaging the set screws that hold the head in place. The damping inherent in the legs can therefore be dwarfed by other design factors of the tripod. Given that we have seen carbon fiber tripods with very low damping, I postulate that the leg materials contribute relatively little to the damping that we typically see in tripods. Carbon fiber does appear to damp better than aluminum though, as expected.

In addition to analyzing the entire database of tested tripods, I have tested four sets of tripods that are identical except for leg material. These provide a much better control for our study. The measured specs for these tripods are listed below. As usual, the reported stiffness and damping are the harmonic mean of the measurements about the two axes.

Tripod | Price | Mean Stiffness Nm | Mean Damping Js | Weight lbs (kgs) |

Manfrotto MT055CXPRO3 | $340 | 1289. | 0.386 | 4.26 (1.933) |

Manfrotto MT055XPRO3 | $230 | 877.8 | 0.200 | 5.50 (2.498) |

Manfrotto MT190CXPRO3 | $330 | 756.6 | 0.177 | 3.49 (1.587) |

Manfrotto MT190XPRO3 | $176 | 519.7 | 0.067 | 4.39 (1.995) |

Manfrotto 190go! Carbon | $280 | 548.2 | 0.148 | 2.97 (1.351) |

Manfrotto 190go! Aluminum | $150 | 482.7 | 0.125 | 3.63 (1.65) |

MeFoto GlobeTrotter Carbon | $350 | 531.2 | 0.166 | 2.97 (1.35) |

MeFoto GlobeTrotter Aluminum | $200 | 495.4 | 0.196 | 3.64 (1.653) |

As you can see from the table, the carbon fiber tripods are roughly 20% lighter, with better stiffness, generally better damping, at just under double the price. There is significant spread between the pairs of tripods with respect the difference in stiffness and damping performance. For the Manfrotto MT tripods, the stiffness and damping is much better for the carbon versions, while for the Mefoto Globetrotter the stiffness is roughly the same and the damping is somehow worse.

This disparity directly is almost certainly a result of the quality of carbon fiber used. The cheap carbon fiber tubes of the Mefoto are significantly lighter than their aluminum counterparts, but don’t actually perform better. The Manfrotto MT tripods have stepped up their game recently, and are clearly using higher quality tubes. This data set is inherently limited to tripods that have both carbon fiber and aluminum versions. All of the most expensive (and highest performing) tripods don’t come in aluminum versions. This denies us the direct comparison of how much better the best carbon tripods can be. However, the stiffness vs weight plot for all tripods above tells us that the performance of carbon is at least several times better. It is no mystery why those manufacturers looking to make the best possible tripods only use carbon.

So far we have only focused on the performance aspects of carbon fiber and aluminum. There are other properties to these materials that affect the use of the tripod. Carbon fiber has much lower thermal conductivity than aluminum. Handling an aluminum tripod on a cold morning can be a truly uncomfortable experience and affect a shoot. The insulating properties of the carbon fiber can make this a non-issue. In a pinch though, so can leg wraps, but these further add to a tripod’s weight. Under severe stress, aluminum deforms while carbon fiber shatters. A bent tripod is still likely useful while a shattered one is not. If damage is a concern for your equipment, this may factor into your choice of material.

In summary:

**Carbon**

- Better Stiffness
- Better Damping
- Lighter
- Lower Thermal Conductivity

**Aluminum**

- Cheaper
- Damage Resistant

Carbon fiber is clearly the better material for tripods. It simply performs at a much higher than aluminum, which was the previous material of choice. Aluminum still has a role to play for economical tripods. It is much cheaper and can be used to provide good value and build quality. If by the end of this article you are still trying to choose between aluminum and carbon fiber, you simply need to decide if the performance gains from carbon fiber are worth the additional cost. And remember, not all carbon fiber is created equal.

]]>From the perspective of the manufacturer, it is certainly appealing to err on the side of narrower leg angle. The tripod will be lighter and/or taller than if the leg splay were wider, padding the spec sheet. In addition, the overall material cost will be a little bit lower. There are strong use reasons not to want the leg angle to wide as well. Too wide of a stance becomes cumbersome and unwieldy. If used in a populated area, the tripod becomes that much more prone to blocking pathways and getting in the way of the photographer. A wider stance tripod is much less prone to tipping over though, and as we shall see, also produces better overall stiffness.

Lets take an overview of the anecdotal evidence referenced above. Below is the ratio of the pitch versus yaw stiffness of each tripod I have tested versus its opening leg angle.

There is a clear upward downward trend as the leg angle opens up. This plot is showing us that there is clearly an effect on the stiffness due to leg angle, but doesn’t say anything about the overall performance of the tripods in question. Clearly though tripods with a wider stance have much better yaw stiffness with respect to their pitch stiffness. On the extremes we have the Feisol CT3442 Tournament and the Really Right Stuff TVC23. The RRS is an outstanding performer, while the Feisol is merely okay. There are a lot of good and bad tripods in between.

To better understand the effect leg angle has on performance, we need to test a single tripod at a variety of different leg angles. The tripod I have chosen for this test is the RRS TVC23 because it has the widest native spread. Thus, by inserting shims between the pull tabs and the apex, I can methodically decrease the leg angle. The shim is simply aluminum foil. This is ideal for being thin and allowing for small angle changes and also for maintaining full metal to metal contact between the leg and the apex.

The bar shown on top is simply the standard test apparatus. After inserting the foil, the angle of each each leg was measured. The results were averaged and that is the reported value for the leg angle. I took three measurements at each leg angle and each one is plotted on the charts below. First, lets take a look at the Yaw Stiffness:

That is a beautiful set of data. All of our suspicions regarding the effects of leg angle on yaw stiffness are confirmed. The yaw stiffness of the tripod increases dramatically as the legs splay out further. Going even from the common leg angles of 22.5 degrees to 25 degrees results in a 15% increase in the yaw stiffness.

The results for the pitch stiffness are decidedly less dramatic. There appears to be a slight increase in stiffness as the leg angle decreases, but its difficult to say as differences aren’t that far above the noise level. If the measured effect here is real, it would be entirely imperceptible in use. I deliberately let the graph continue all the way down to zero to emphasize how little effect is seen here. If I were able to test larger leg angles than the native 26.5 degrees on the TVC23, I would expect the stiffness to fall off eventually. The above data encompasses the entire normal range of values found on tripods for the primary leg angle though, so one would have to be using the tripod with the legs splayed out to a different setting to see an effect.

If we construct the same plot as the first one looking at the ratio of the stiffness with the TVC23 data, we get:

The overall trend is clearly the same, though from the data we know that the effect is dominated by the change in yaw stiffness.

There is some clear structure to the damping data, but not quite as clear as the stiffness. This is a direct result of the damping measurement being much noisier and that the damping behavior is less linear than stiffness. At any rate, there is a clear drop off in the yaw damping to accompany the drop off in yaw stiffness as leg angle decreases. The difference is not as large though.

The implications here are non-trivial. Wider leg angle results in better tripod performance. Clearly there are good reasons to use a narrower leg angle. A narrower angle improves the height/weight ratio and reduces the overall footprint. This last point is not inconsequential when using the tripod in confined or crowded spaces such as a studio, busy street, or crowded viewpoint. The optimal leg angle for a tripod then becomes somewhat subjective. It depends on the application and preference of the user. Those looking to optimize performance may want a wider leg angle, while others may want the more compact package of a narrower one.

For me, I prefer a wider leg angle. For example, lets consider two hypothetical tripods that are otherwise identical except one has a leg angle of 22.5 degrees, and the other is at 25 degrees. The data above shows that the second one would be roughly 15% stiffer in the yaw direction, which is the weakest and therefore the most critical direction of motion. Using a little trigonometry, we can see that this second tripod would only be 2% shorter than its 22.5 degree sibling. That’s a trade off I would happily make.

It would be interesting to see how other tripods perform under the same test. The results here are so strong though that I doubt the conclusion would be any different. Tripods are mostly built in the same way. At some point I also want to test the stiffness beyond the maximum 26.5 degree leg angle if the RRS TVC23. This will require something more complicated than simply using some aluminum foil shims, such as 3d printing some custom pull tabs. So that is a project for down the road.

]]>The test setup is pretty basic. I am using the same Gitzo GT5533LS tripod used for the stiffness test as it is the most stable platform I know of. This simply minimizes the chance that the tripod gets bumped or moved during the test. On top of the head is a laser that points to a far wall. It certainly doesn’t need to be a great laser, but it is useful to have something that is well collimated to provide a small spot size.

The test procedure is also pretty simple. I loosen the ball head so that it has just enough tension to keep the laser from moving. I then mark the position of the laser spot on the far wall and tighten the ball lock mechanism, marking the spot position again. The angle of deflection is thus given by

where is the change in the spot position and is the distance from the center of the head to the wall. I am implicitly using the small angle approximation here as is very small compared to .

I am measuring the deflection of the head for four different orientations of the ball head so as to average over any asymmetries. Shifts in the roll direction from the camera’s perspective will cause much less deflection than shifts in the pitch or yaw directions. Which direction is pitch and which is roll from the ball head’s perspective isn’t constant though, and thus the need to rotate the head between measurements.

The raw data is shown below. I tested three heads, the RRS BH-55, Arca Swiss Z-1, and Acratech Ultimate. The lock mechanism for each of these heads is quite different, and we see quite different results. The Acratech clearly performs the worst of the bunch.

The deflections in mm and the resulting shifts in degrees are presented in the table below. The ball head center was at a distance of 5.22 m from the wall.

RRS BH-55 | Arca Swiss Z1 | Acratech Ultimate | |

0 | 8.94 | 14.96 | 19.36 |

90 | 2.1 | 4.84 | 24.26 |

180 | 11.26 | 12.76 | 16.29 |

270 | 11.83 | 3.65 | 17.67 |

Average | 8.5325 | 9.0525 | 19.395 |

Degrees of Shift | 0.09 | 0.10 | 0.21 |

Since I have only tested these three heads, I don’t have a lot of data to put these results in context. Clearly the shifts are small and would not impact most photography. In critical situations with telephoto lenses though, they might

There is a little bit of randomness in how much shift occurs on each trial. I estimate that the amount of shift varies by 25% or so between iterations at the same orientation. To get a more accurate assessment for each head, I would ideally take 10 trials at each orientation to get an average and standard deviation. I am not going to do that since it would take too much time. So, the results will have to be taken with a grain of salt, but should give a decent idea of how much shift to expect, and hopefully identify the worst offending heads. Look for these results to begin appearing on the review page for each head.

]]>The first change I have made is that I now report the average stiffness in the yaw and pitch directions. While most tripods have a pitch stiffness of about three times the yaw stiffness, there are some that deviate significantly from this. I have some anecdotal evidence that this is related to the leg angle. Thus only reporting the yaw stiffness is leaving out some important information. I am not using a simple average of the two stiffness numbers, but instead the harmonic mean. This averages the reciprocals and arrives at a much more sensible metric for our purposes. If the stiffness in the two directions is the same, then mean is just reported as that number. Say however, the stiffness in the yaw was given by X, and the pitch stiffness was infinite. A simple mean would report infinity as the average, where the harmonic mean reports 2X. The harmonic mean is dominated by the lower of the two stiffness numbers. This is ideal for us where the yaw stiffness is much lower than the pitch stiffness. The flexibility of the tripod is predominantly in the yaw direction and that is thus where our focus is, but the pitch direction is important as well and thus gets factored into our score calculation.

The second change is in regards to how the height of the tripod is factored into the score. I have done a study on how tripod stiffness varies with the height of the tripod. I found that when approximating the stiffness vs height of a tripod, the optimum height exponent to use if only one data point is available is -1.24. An exponent of -1.4 fit the data better over a narrow range about the maximum height. To compensate, I am going to use the exponent of height^1.25 in my rankings. I am going with this this value as it is a nice round number, and more closely backed by the empirical fits to the data. The adjustment will be less accurate over small changes in height than a 1.4 exponent would have been, but is more accurate over larger changes in height. Also, it turns out that both of these exponents produce very similar rankings, and it doesn’t matter that much which is used. So I chose to go the more conservative, less subjective route.

I haven’t touched the weight component of the score metric. I still simply divide by the weight. In reality, there seems to be a stronger than linear correlation between the stiffness and weight, as shown in the plot to the right. This makes sense. The stiffness of a tube scales as the diameter^3 but the weight only scales as diameter^1. Although clearly much of the tripod weight is not in the leg tubes. When accounting for height as above, we are effectively asking what the stiffness of a tripod with shortened legs would be, given that the only data point we have is the stiffness at the maximum height. Such an approach makes no sense when applied to weight. The weight of the tripod is the same no matter how you use it. We don’t want to completely ignore weight though, as it is very clearly an important factor that matters to a lot of people. The problem though is that it matters differing amounts to different people. Thus, I am leaving scaling of the score with weight the same as before, with an exponent of -1, or in other words, simply dividing by the weight.

The full score metric is thus given by:

These are of course not the only important factors of choosing a tripod. I am not trying to approximate the utility functions of tripod users, which of course will be wildly different, but provide some simple metric to rank tripod performance. It should be used as a guideline for finding the best performing tripods, but not used as the sole purchasing decision. Hikers may value low weight much more than stiffness. Studio shooters may not care about weight at all. The folded length of the tripod is critical for travelers. Price isn’t even addressed here at all. There is a lot more that goes into selecting a tripod than can be captured in single metric. I just hope that the rankings page provides a decent starting point.

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I simply do not have the time to measure the stiffness vs height for each tripod I test. As we have seen in this series though, tripods perform much better at shorter heights. For two tripods that are otherwise identical in construction except for height, the taller one will perform worse simply because it is easier to bend a long beam (tripod leg) than a shorter one. To construct the tripod rankings score, I thus want a simple metric that rewards taller tripods versus shorter ones. The taller tripod could of course be used at a shorter height, with a corresponding gain in stiffness, and we don’t want to unduly penalize it just for being tall. In fact, you may want to reward it for its increased versatility, but I don’t want to assign any value judgments. I just want to level the playing field in the most numerically backed way possible.

In the previous posts, I fit the stiffness vs height data to some simple functions that best approximated the height over the tested range. I am going to simplify things further. I am going to force my fit to go through the data point corresponding to the tallest height, and then fit the powerlaw function:

Now though, $\kappa_0$ is not a free parameter, but fixed the above constraint such that:

So we now have one fewer degree of freedom. The resulting fit looks like:

I have added to the graph five curves corresponding to what the fit would look like for a variety of other possible exponents. All of the curves pass through the point corresponding to the maximum height, as they are constrained to do. The exponent that creates the best fit to the data, according to a least squares optimization, is -1.29. However, we can easily see that for the upper ranges of the tripod height, the exponent of -1.50 provides a much closer fit to the data. This is important because this is the range in which we are more interested in normalizing the data. We would never care about comparing this tripod to one that is less than 0.75m in height, where the -1.50 line diverges from the data. However, in a ranking that involves tripods of wildly differing heights, an exponent of -1.50 may be too generous to tall tripods.

Below is a list of the exponent fitted in the same manner as above, for all of the tripods I have data for stiffness vs height. I also added the exponent for the fit that I felt best approximated the behavior around the maximum height, but diverged for lower heights.

Tripod | Fitted Exponent | Eyeballed Exponent |

Sirui T2205X | -1.11 | -1.5 |

Oben CT2491 | -1.35 | -1.5 |

Gitzo GT2542 | -1.18 | -1.5 |

MT055XPRO3 | -1.35 | -1.5 |

MT055CXPRO3 | -1.25 | -1.5 |

MT055CXPRO4 | -1.36 | -1.5 |

RRS TFC14 | -1.29 | -1.5 |

RRS TVC23 | -1.13 | -1.13 |

RRS TVC24L | -1.30 | -1.5 |

RRS TVC33 | -1.13 | -1.25 |

RRS TVC34L | -1.15 | -1.25 |

Average | -1.24 | -1.42 |

The behavior of these tripods is pretty similar to one another. The plot generated for each tripod can be found at the bottom of the post. These averages present lower and upper bounds for what the exponent used in normalization should be, and fortunately, it is a pretty narrow range. We aren’t going to see massive swings in the rankings based on what exponent is chosen. If you have thoughts on where in this range the normalization exponent should be chosen, please say so in the comments. I will be mulling this over before choosing a value to reconstruct the rankings page.

Appendix: Data to make your own judgement

]]>These are very similar to the other RRS tripods in terms of the fitted exponents and for the TVC34L, the apex stiffness. The fitted apex stiffness for the TVC24L is quite different from the TVC-23, which came in at 9504, as opposed to the 5814 seen here. Given that the apexes for these two tripods are actually identical, this reinforces the notion that this fitted number does not actually reflect the stiffness of the apex, but instead some other undetermined aspect of the tripod. The factor is still clearly important towards getting a good fit.

Now lets overlay the data for the similar tripods:

This is awesome. In each case, the stiffness of the four section long version closely parallels the stiffness of the three section version where they overlap. The three section versions are a little bit stiffer. This is likely due to the fact that the four section version still uses some of its weakest bottom leg section when extended to the same height as the three section version. The leg sections of the four section versions are slightly shorter due to adding a section, even though the tripods have similar overall folded length.

So, if you need the height of the long version occasionally, but will most use the tripod at the same height as the three section version, fear not. The stiffness numbers are quite similar at the same height. The four section versions are slightly heavier and more expensive, and slightly less stiff. These are small trade offs though given the added versatility, and I thus expect the long versions to be very popular.

]]>I am going to test the stiffness and damping performance for five different top plates, shown above. On the upper left is the original Gitzo plate that came with the tripod new. To the right is an old gitzo plate that has no pad; it is just coated metal. The top right plate is a Desmond plate, with a set screw and a very hard piece of plastic on top. The lower left is a LeoFoto plate compatible with the gitzo series 5 tripods. Like the new Gitzo plate, it has a soft plastic pad on top. Finally, in the lower right is a custom machined solid aluminum plate with no sort of coating.

The stiffness and damping for both the yaw and pitch directions are shown below:

Yaw Stiffness Nm/rad | Yaw Damping Js/rad | Pitch Stiffness Nm/rad | Pitch Damping Js/rad | |

New Gitzo | 3630 +/- 10 | 1.13 +/- 0.11 | 8222 +/- 22 | 0.94 +/- 0.09 |

Old Gitzo | 3713 +/- 4 | 0.46 +/- 0.05 | 8194 +/- 10 | 1.26 +/- 0.12 |

LeoFoto | 3856 +/- 17 | 1.09 +/- 0.11 | 8010 +/- 24 | 1.35 +/- 0.13 |

Desmond | 3651 +/- 10 | 0.86 +/- 0.09 | 7623 +/- 16 | 1.17 +/- 0.11 |

Custom Aluminum | 3739 +/- 5 | 0.44 +/- 0.04 | 7810 +/- 9 | 1.19 +/- 0.12 |

The differences in stiffness are not particularly dramatic between the tripod plates. While the differences are statistically significant, they are too small to notice in use. I don’t see any particular rhyme or reason as to which plates are the stiffest. I expected that the two plates without a pad would be slightly stiffer, but that does no appear to be the case. The old Gitzo plate, or perhaps the LeoFoto plate appear to be the stiffest overall, but by a very small margin.

The differences in damping are quite significant in the yaw direction. We can see that the two plates without a pad had much lower damping than the other three, as expected. The Desmond plate, with its much harder plastic pad, performed in between the aluminum ones and the softer plastic pads of the new Gitzo and LeoFoto plates. In the pitch direction, there isn’t a statistical difference between the plates, indication that the damping is occurring in the legs.

The clear choice for testing heads going forward is the custom aluminum plate. It isn’t different from the old Gitzo plate in terms of performance, but being able to tighten the bolt with a hex key from below is a huge advantage. It significantly helps with the workflow and prevents the head from becoming stuck onto the top plate. There is still a decent amount of damping in the system. Ideally I would build a custom head testing rig out of aluminum or steel, which would have much lower damping. The Gitzo will do just fine for now though.

Here is some of the raw data used to take this measurement. We will only be looking at the yaw oscillations.

Custom Aluminum Plate:

Gitzo Old Plate:

Desmond Plate:

LeoFoto Plate:

Gitzo New Plate:

The oscillation frequencies are all very similar. The much more noticeable affect is the damping, in which these data have been arranged from least to most. The only reason that the damping rates are in the seconds scale is that I am using a lot of rotational inertia to make these measurements, similar to the largest telephoto lenses available. The damping would feel nearly instantaneous for any normally sized camera gear.

So, we have learned that the top plate can have a very significant impact on the damping performance of the tripod as a whole. This is the first place to look if the tripod has too much or too little damping. The stiffness was affected slightly, but not in a way that would be noticeable without specialized test equipment.

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Enter the Manfrotto MT055 tripods. I happened to have both the carbon fiber MT055CXPRO3 and aluminum MT055XPRO3 versions on hand, each with a center column material to match the legs. I decided to do the same stiffness vs center column height test for the aluminum and carbon center columns, both while installed on the carbon fiber CXPRO3 legs. The apexes are identical for both tripods, so it shouldn’t matter which tripod the test is conducted on. Using the stiffer carbon legs simply accentuates the flexibility of the center column. Here are the test results as I traditionally present them:

It is immediately obvious that aluminum center column performs better in the yaw (horizontal) stiffness. The pitch (vertical stiffness) is harder to see. So lets compare the results in a more natural way for this test, head to head. Here is the yaw stiffness:

That is a dramatic difference. The loss of yaw stiffness after raising the center column to maximum height is pretty minor, only 29%, compared to a 65% loss of stiffness for the carbon fiber center column. The aluminum center column is dramatically outperforming the carbon fiber one.

The results for the pitch stiffness are much less dramatic, and pretty similar to each other. Both tripods lose about 70% of their pitch stiffness when the center column is extended to maximum height, with the aluminum one losing a couple percentage points more.

There is a simple explanation for what is going on here. The stiffness of carbon fiber is directional. Carbon fiber tubes for tripods are manufactured primarily to resist bending, not torsion. This becomes immediately apparent when using the carbon fiber for a center column, where torsion stiffness is the primary factor for the yaw stiffness. For the pitch stiffness, in which the center column experiences bending, the carbon fiber still outperforms the aluminum. The stiffness of aluminum is isotropic, or doesn’t vary depending on direction. It should thus come as no surprise that the aluminum outperforms the carbon fiber in the direction that the carbon fiber wasn’t designed to be stiff.

This brings up the natural question, why don’t manufacturers use aluminum instead of carbon fiber in the center columns of their carbon fiber tripod? Clearly aluminum appears to be the better choice from a stiffness perspective. The weight difference is negligible. I measured it at 15 grams, with the aluminum of course being heavier. The increase in stiffness is plenty to justify that weight increase. This leaves us with some poor explanations. Perhaps some tripod manufacturers simply are unaware, and simply use carbon fiber because everyone says its better. Perhaps they know aluminum is better but that their customers think carbon is better, so use carbon.

The opportunities to improve center column performance are apparent. One can use thicker carbon fiber tubing on the center column compared to the rest of the tripod. The same applies to aluminum. One could also use a different weave of carbon fiber. Carbon fiber tubes can be made to resist torsion, such as in the use of carbon fiber driveshafts. Surely a weave could be found that better optimizes the stiffness performance in both torsion and bending. The center column appears to be an aspect of tripod design ripe for innovation.

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Without further adieu, here is the stiffness vs height data for the Gitzo GT2542 Mountaineer tripod.

The GT2542 is a four section tripod, so I expected the magnitude of the exponents to larger than for three section tripods. Quite the opposite here. The exponents are lower in magnitude than we saw for the Manfrottos. My best guest for this is that Gitzo’s new “Exact Carbon Fiber” legs use a thicker diameter bottom leg section compared to the upper sections. This will make the stiffness of the leg more uniform throughout, and lower the magnitude of the exponent. Again we can see the model with an added finite stiffness term performs better, but it is a little less dramatic than with the Manfrottos.

The Oben was quite a surprise. I specifically chose this tripod as it has a very weak center column locking mechanism. With the twist lock fully tightened down, one can still rotate the center column by using a little leverage. I thus expected the apex stiffness to be low, which is clearly not the case. So, either my impressions of what constitutes a stiff apex are wrong, or the constant stiffness term isn’t actually reflective of the apex stiffness. The answer is probably a little of both, but I don’t know. If the legs don’t behave according to a simple power law, any error in that assumption will show up in that constant stiffness term as I currently have things set up. Assuming that it is reflective of the apex stiffness, the good news and bad news for the Oben is that most of the flexibility comes from the legs. But those legs are not particularly stiff.

Also, note how close the two fits are to each other despite having a different exponent. There is a lot of error fitting this type of data, so take the fitted parameters with a big grain of salt. These are useful for ballpark estimates, not nitpicking over small differences between tripods. Technically speaking, there is a significant amount of covariance amongst the fit parameters. This is in contrast to fitting the frequency in the individual stiffness tests, where the fitted frequency is very accurate and not related to the other fit parameters.

I chose to test this tripod, as it was the only five section tripod I had on hand, and would thus provide the greatest range of heights. The results are less interesting that I had hoped, with one of the flattest curves I had seen among the data. The tripod is simply not very stiff all around, and it shows. This tripod had one of the biggest disparities between the power law fit for the two models, which makes sense given it has the lowest apex stiffness of any tripod I tested.

I chose the RRS TVC-33 hoping that it would show a nearly infinite apex stiffness due to having no center column. Definitely not the case. This is the best evidence I have yet that the constant stiffness term may not actually the apex stiffness, but more complicated aspects of the stiffness in the legs as well. Clearly the constant stiffness term is necessary to accurately describe the data in this case.

The behavior of the TVC-23 is much closer to what I expected from the TVC-33. There is very little to choose between the two models because the fitted value for the apex stiffness is relatively high. Note again how much of a difference there is in the exponent between the two models, despite looking very similar in the plot. Take the fitted exponent number with a big grain of salt

The TFC-14 shows a lower apex stiffness than I expected given that the apex is just a chunk of aluminum. It could be that the coupling between the apex and the camera bar I use for testing wasn’t great due to the very small size of the TFC-14 apex. Again, it could also be that the ‘apex stiffness’ term is actually just capturing some complex aspect of the leg behavior.

These results answer some questions and leave some others open. Most notably, the apex stiffness constant term does not seem to provide results consistent with what I expect from real world observation of tripod construction. The motivation behind the term is clear. A simple power law would give infinite stiffness for a tripod as the leg length went to zero. The actual stiffness at a hypothetical zero leg length should be some finite value. The term clearly results in better fits as well, but is likely not the only way of adding a parameter to improve the fit. I wish that I could adjust the leg length over a much wider range, as this would allow better discrimination between models

One of the main motivations of this work was to find a simple way to compensate height when comparing the stiffness of tripods. Because I am not going run a stiffness vs height test for every tripod, I won’t have the constant offset ‘apex stiffness’ term. Looking at only the simple power law fits, we can see that an exponent of -1 is a pretty reasonable and simple guess for the power law behavior. Obviously it is far from perfect and suits some tripods much better than others. It represents the TVC-23 very well, and other tripods to varying degree.

In terms of modeling tripod behavior, this data set also places an upper limit on the magnitude of the exponent. The exponents measured here are coming in significantly lower in magnitude than -2. The lower sections of tripod legs are less stiff than the upper ones, so we should expect the magnitude of the exponent to be higher than for a simple constant stiffness leg. These factors lead me to believe that the correct exponent for a constant stiffness leg is -1. This follows the stiffness behavior we would expect from a cantilevered beam with an end moment, which also happens to look like a reasonable model.

]]>Here is the same data for yaw stiffness vs height for the aluminum MT055XPRO3 that we saw in the last post:

As before, we can see that including the term for the finite apex stiffness significantly improves the appearance of the fit. This is particularly evident at the edges of the data set.

The MT055CXPRO3 is identical in construction except for the use of carbon fiber in the legs and center column. The results are rather similar. Because the stiffness starts out a lot higher at max height, the carbon version shows a much flatter curve. The apex stiffness plays a larger role. The apex stiffness is lower than I expected, but still within ballpark of the aluminum version of the tripod. Take the exact numbers for the fits with a grain of salt. There is a lot more error with these parameters when compared to fitting the tripod resonance frequency in the individual stiffness tests. There is also significant covariance between parameters in the fit. By this I mean we could obtain a nearly equally good fit by raising the apex stiffness slightly and lowering the magnitude of the power law exponent slightly. This would make it look much more similar to the aluminum version in behavior. I am not reporting the errors here, because to do a full error analysis would require the entire covariance matrix for the fit, which is beyond the scope of this article. Just take the numbers as approximate. The power law exponent is around -2, not exactly -2.16.

The data for the four section MT055CXPRO4 is remarkably similar to the aluminum version. The apex stiffness for both is right around 4000, and the exponents are incredibly similar. Again, the stiffness is a little bit higher throughout, so the curve is flatter, and more similar to the other three section carbon version.

Based on this data, these fits seem to give a ballpark estimate of the apex stiffness and how much it impacts the stiffness of the tripod overall. The exponent for the leg stiffness vs height seems to be hovering right around -2. Given that the least stiff bottom legs of the tripod collapse first when reducing height, we should expect that the exponent for a tripod with a single leg section to be lower in magnitude, say between -1 and -2. While such a tripod of course would be impractical, it forms the basis simple modeling of tripod behavior. Basic beam deflection formulas typically assume that the beam is of constant stiffness, which multi-section tripod legs clearly are not. These data definitively rule out any model with an exponent of -3, and most likely ones with an exponent of -2 as well. Tests of stiffness vs height for more tripods is forthcoming, and eventually a discussion of a deflection model for tripods.

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