It is impractical to look at the style of chart presented in part II, with one chart for each tripod, and try to draw any meaningful generalizations. Instead, here I am going to calculate the optimal ball head for each tripod, and see how each compares to its tripod. I am going to use the ‘good ball head’ model from part I. If I used only the ball heads that I have tested, the optimal head for each tripod would always be one of the top three performing ‘outlier’ heads discussed previously. Thus, the good ball head model will allow for a more continuous result. Needless to say, all of this analysis is pretty rough and we are throwing various approximations around. The goal here isn’t to get absolute precision, but simply to understand the rough range of ball heads one should be looking for.

For each set of tripod legs that I have tested, I calculated the optimum ball head. The relative stiffness’ of the head and legs is shown in the plot below. Each blue dot represents a tested tripod.

We can see that there is a clear relationship between the stiffness of the tripod and the stiffness of the optimal head for that tripod. That relationship isn’t a perfect line though, there is a significant spread. Now, there is one important factor that isn’t displayed in the chart above, and that is the weight of the tripod. (We are assuming a constant stiffness/weight ratio for the ball heads). Below is the same chart but now color coded according to the stiffness/weight ratio of the tripod. The two best performing tripods have been removed to make the rest of the data more visible.

The redder the dot, the better the stiffness/weight ratio of the tripod. What we are seeing is that the higher the stiffness/weight ratio for the tripod, the more sensitive it is to the weight of the head. For heavy tripods, the optimal head is also much heavier because it doesn’t adversely affect the weight of the entire system as much.

Plotting some trend lines on the graph, we can see that the best tripods are optimized with a good head around three times the stiffness of the tripod, and the worst around six times the stiffness.

So, our takeaway is that you should be looking for a ball head that is a minimum of three times the stiffness of the legs. If you don’t have the absolute best legs, this number bumps up a little bit. Its also worth noting that these optimums exist on top of a fairly broad and flat distribution, as seen in part II of this series. It tends not to matter too much if you get a head that isn’t quite at the optimum. I recommend erring on the stiffer side, as bigger ball heads tend to have better ergonomics. Also, if you are really looking to eke every possible gain out of the stiffness/weight ratio of the combined tripod-head system, it is more important to get a head with a good stiffness/weight ratio than getting the head/tripod stiffness ratio perfect.

]]>Before diving in, we need to be clear about exactly what we are optimizing. In engineering, this is called choosing a ‘figure of merit’ (FOM). I propose that we want to maximize:

where is the total system stiffness and is the total system weight. This is the same FOM as used for the head rankings page, but doesn’t factor in height as the tripod score metric does. This is because there is very little variation in head height compared tripod leg height. We are thus implicitly making the approximation that all heads are the same height, at least when compared to the tripod legs. As implied by the title, we are optimizing the choice of ball head, not the tripod. The assumption here is that you have a set of legs in mind for which you are trying to choose a head, and thus the height of the total system is effectively already set. The weight and stiffness are the remaining degrees of freedom.

To calculate the stiffness of the tripod + head system, I am simply adding their stiffness’ as one does springs in series. This was shown to work well in a previous post, outlining the technique. I am then taking the harmonic mean of the total system pitch and yaw stiffness’ to get an overall average stiffness metric, which is then simply divided by the combined weight of the tripod and head. For a given tripod, I calculate this FOM for each ball head that I have tested. The optimal ball head is then simply the one with the maximum value for the FOM.

Now, I could simply give a sorted table showing the FOM with each head, but tables are boring and hard to read. Instead, I plot the FOM for each head versus the weight of that head. We should then be able to see in a nice visual way that smaller, weaker tripods only need a small, lightweight head while heavy, stiff tripods benefit from a stiffer head despite the added weight that such a head incurs. This is a bit awkward, as I could have alternatively plotted against the stiffness of the head. There isn’t a strong justification for choosing one over the other in this case. However, as shown in the previous post, the stiffness and weight for the best heads are approximately proportional, so it matters very little which I choose.

Speaking of which, we can construct a model “good ball head” based on this proportionality. This head is can be any weight, but has the yaw stiffness of 15,000 Nm per kg and pitch stiffness of 8,000 Nm per kg fitted in Part I. This head is plotted for every weight as a red curve in the plots below.

Let’s finally look at some results!

**Really Right Stuff TFC-14**

My canonical guinea pig tripod, the TFC-14 is relatively strong for its weight, so we should thus expect it to be somewhat sensitive to both the weight and stiffness of the head.

Again, the blue dots represent each ball head that I have tested. The higher up on the chart, the better the combined stiffness / weight performance of the head – tripod system. The red line represents the “good ball head” model described above. The results are precisely what we should expect. A weak head will compromise the stiffness of the system. At some point though, there are marginal gains from to be had from increasingly stiffer heads, and those heads just add weight. Intuitively, this makes sense. There is no point in putting a massive head on a small set of legs.

There are three heads that lie above the red curve. These are the same as we saw in the previous post, from left to right on the chart, the RRS BH-25, Sirui K-30X, and Feisol CB-70D. While the BH-25 is the optimal head (of those that I have tested) for the TFC-14 legs from a stiffness/weight point of view, this analysis leaves out a lot of information. This is not a review or endorsement of the BH-25. The head is tiny, has no panning lock or tension control, and awkward ergonomics. The head that I use with these legs is the Sirui K-10X, which is the head lying on the red curve at the maximum. But again, I’m not trying to make specific recommendations in this post, just observe some trends.

**Really Right Stuff TVC-23**

In a similar vein, the TVC-23 is also very stiff for its weight, but a significantly stiffer, larger tripod than the TFC-14.

The story here is similar, but we now see that the tripod is less sensitive to the head’s weight, and more sensitive to its stiffness. There is no clearly optimal range for the head choice. It is still important to choose a good head, but one might choose a lighter one if the intended use is travel, or a heavier stiffer on for the studio.

**Gitzo GT5533LS**

This is the strongest tripod I have tested, and thus should want to have the strongest ball head.

This set of legs does indeed benefit from the stiffest available heads. The legs are heavy enough to begin with that the added weight from such heads isn’t an issue.

**Manfrotto BeFree Advanced**

Now for a relatively light and weak tripod

The effect here is a little more dramatic. The weakness of the legs means that it is pretty pointless to pair them with all but the lightest heads. This is the trend I have seen with all of the weaker tripods. Don’t bother with big stiff head.

Most other tripods fall into the general categories seen above. For a lot of the legs in the mid stiffness range, the plot looks pretty similar to that of the TVC-23, or pretty flat for most heads with good underlying stiffness to weight ratios. For the weaker tripods, don’t bother pairing them with a big stiff head. For the sturdiest tripods, get a big stiff head to get the most out of your legs.

I think I will start adding this analysis to tripod reviews and build out a recommended heads page for each tripod. This will clearly evolve as more heads get tested, but the already tested heads represent a decent starting point.

]]>

The only thing we are going to do in this first post is look at the general trends of stiffness vs weight of ball heads. This will become important later on. For now though we are just exploring the limits of what kind of performance we can expect on a weight adjusted basis. Diving right in, here is the yaw and pitch stiffness of every ball head I have tested against its weight:

The farther up and to the left (stiffer and lighter respectively), the better the performance. Immediately obvious is that the pitch stiffness of most heads is worse than the yaw stiffness. I’m not exactly sure why this is, but I suspect that it has to do with the stem between the ball and the quick release clamp. There is significant asymmetry here in the way that the stem bends under load. Yaw motions are torsional, while pitch deflections are of a beam deflection type. Tripods tend to be the opposite, with the pitch motions being stiffer than yaw.

The other apparent feature is that there is a strong linear relationship between the weight and the stiffness. There is no reason this should necessarily be the case, but this could be a useful feature to take advantage of in our future analysis. I have drawn two lines on the plot, roughly through the best performing heads. In yaw, the best performers seem to have stiffness around 15,000 Nm/rad per kg, and in pitch, that stiffness is around 8,000 Nm/rad per kg.

Note that a head that performs well in yaw stiffness, also tends to perform well in pitch stiffness and vice versa. So it doesn’t appear that there is a trade off between the two. There are three heads that stand out as particularly high performers. These are the RRS BH-25 on the light end, the Sirui K-30X in the middle, and the Feisol CB-70D on the high end. We will continue to see these heads pop up throughout this series of posts.

A plot of the mean stiffness vs weight tells a similar story as above:

Again we see those three outstanding heads well above the general trend. I have also plotted the three pan-tilt type heads that I have tested in green. The performance is very poor compared to every ball head. There are very good reasons to use pan-tilt heads, but optimizing your stiffness/weight isn’t one of them. That is why I am only including ball heads in this exploration.

Finally, while we are here, we can also plot the stiffness vs. the diameter of the ball as opposed to weight:

This is the harmonic mean of the pitch and yaw stiffness’. We can see again, to no surprise, that there is a strong relationship between the stiffness and the size of the ball. Bigger is better. We see fewer high performing outliers as before as all the top performing heads lie along a fairly consistent line. This indicates that they key to outstanding performance from a stiffness/weight perspective is packing a big ball into a compact and lightweight package. The RRS BH-25 is the epitome of this philosophy. The head has no tension control or separate panning lock, reducing the overall weight.

We have seen that for the best ball heads, the stiffness of the head is roughly proportional to its weight. Weight isn’t what gives the head stiffness, as we have seen plenty of heavy and not stiff heads, but there seems to be a practical upper limit to the achievable stiffness. This trend is going to be a useful reference point going forward for both calculating and making sense of the optimization results.

]]>

The stiffness measurements for tripods legs and heads taken on this site are thus done separately. Testing each combination of head and legs would be totally impossible. In practice however, tripod legs and heads are used in conjunction as a single system. We thus need a method for calculating the combined stiffness of the system. Fortunately, summing the stiffness of springs in series is well understood and fairly straightforward. The stiffness of the total system can be expressed as the reciprocal sum of the head and leg stiffness’, as follows:

where is the stiffness constant. A trivial bit of algebra then yields:

In theory this is great and all, but how well does this work in practice? The stiffness of the head is initially measured by applying the above formula with the head on a very stiff tripod, as described in a previous post. So, any reader is justified in being skeptical that this will work well in the real world where we aren’t working with ideal springs. There are a variety of confounding factors such as the myriad of different top platforms on tripods that the heads mate to.

To put the above formula to the test, I measured the yaw and pitch stiffness for four tripod legs and four heads, for a total of 16 different combinations. I endeavored to choose a range of stiffness’ on each such that we would have weak heads on strong legs, strong heads on weak legs, and ones that were appropriately matched. I calculated what the above formula suggests the tripod + head stiffness should be, as the ‘theoretical’ result, and compared that to the measured combined system stiffness. The results are in the table below. As always, the units of stiffness are in Nm/rad.

Legs | Leg Yaw K | Leg Pitch K | Head | Head Yaw K | Head Pitch K | Theory Yaw K | Meas. Yaw K | Theory Pitch K | Meas. Pitch K | Yaw Error | Pitch Error |
---|---|---|---|---|---|---|---|---|---|---|---|

Manfrotto 190X | 403 | 1447 | Sirui K-30X | 9286 | 4965 | 386.2 | 383.6 | 1120.5 | 995.7 | 0.68% | 11.13% |

Manfrotto 190X | 403 | 1447 | RRS BH-30 | 2912 | 2032 | 354.0 | 338.3 | 845.2 | 829.7 | 4.44% | 1.83% |

Manfrotto 190X | 403 | 1447 | GH1382TQD | 1295 | 982 | 307.4 | 300.2 | 585.0 | 555.7 | 2.33% | 5.01% |

Manfrotto 190X | 403 | 1447 | MH 482 Micro | 236 | 334 | 148.8 | 153.6 | 271.4 | 285.3 | -3.20% | -5.14% |

Manfrotto Befree Advanced | 184 | 618 | Sirui K-30X | 9286 | 4965 | 180.4 | 184.9 | 549.6 | 394.5 | -2.48% | 28.22% |

Manfrotto Befree Advanced | 184 | 618 | RRS BH-30 | 2912 | 2032 | 173.1 | 176.9 | 473.9 | 382.4 | -2.22% | 19.30% |

Manfrotto Befree Advanced | 184 | 618 | GH1382TQD | 1295 | 982 | 161.1 | 151.2 | 379.3 | 271.5 | 6.15% | 28.42% |

Manfrotto Befree Advanced | 184 | 618 | MH 482 Micro | 236 | 334 | 103.4 | 104.6 | 216.8 | 194.2 | -1.17% | 10.43% |

RRS TVC-33 | 1509 | 3949 | Sirui K-30X | 9286 | 4965 | 1298.1 | 1302.8 | 2199.5 | 2145.4 | -0.37% | 2.46% |

RRS TVC-33 | 1509 | 3949 | RRS BH-30 | 2912 | 2032 | 993.9 | 912.2 | 1341.6 | 1146.9 | 8.22% | 14.52% |

RRS TVC-33 | 1509 | 3949 | GH1382TQD | 1295 | 982 | 696.9 | 676.7 | 786.4 | 709.1 | 2.90% | 9.83% |

RRS TVC-33 | 1509 | 3949 | MH 482 Micro | 236 | 334 | 204.1 | 196.3 | 308.0 | 293.9 | 3.81% | 4.56% |

RRS TFC-14 | 703 | 2521 | Sirui K-30X | 9286 | 4965 | 653.5 | 643.8 | 1672.0 | 1475.8 | 1.49% | 11.74% |

RRS TFC-14 | 703 | 2521 | RRS BH-30 | 2912 | 2032 | 566.3 | 535.6 | 1125.1 | 1087.8 | 5.42% | 3.32% |

RRS TFC-14 | 703 | 2521 | GH1382TQD | 1295 | 982 | 455.6 | 440.7 | 706.7 | 677.7 | 3.28% | 4.11% |

RRS TFC-14 | 703 | 2521 | MH 482 Micro | 236 | 334 | 176.7 | 179.9 | 294.9 | 294.3 | -1.82% | 0.21% |

Not too bad! The median magnitude of the error in yaw stiffness is 3% and for pitch stiffness, 7%. This means that the springs in series formula works quite well here, and will be a useful tool going forwards. There are some noticeable outliers though, in particular with the pitch stiffness on the Manfrotto BeFree Advanced. I suspect that the center column locking mechanism on this tripod is subpar. The additional height of the head then causes the torque placed on the center column lock to magnified when placed under load. The simple approximation of springs in series clearly breaks down in this case.

Most of the error is on the side of the system being slightly weaker than predicted. This isn’t too surprising. When the heads are tested they are secured to the solid aluminum top plate of the underlying tripod with a 3/8″ bolt and a hex wrench from the underside. This is a stiffer connection than the average tripod can provide. In addition, when testing the legs, the camera bar is torqued down much harder and and has a larger contact patch than most heads. Since the real life connection between the legs and the head isn’t as ideal as the test scenarios, we might expect that the stiffness suffers a bit.

There is another approximation that is implicit in the testing but that is working against us in a small way here. When I test tripod legs and heads, I ignore the moment of inertia of the leg or head itself when calculating the stiffness from the resonance frequency. This is simply because I don’t have a good way of estimating the inertia of the legs or head as I do with the camera bar and weights used for the test. I validate this approximation by using vastly more inertia in the camera bar and weights than can be in the tripod or head, and so the resulting errors are <1%. However, the error is additive when testing the tripod and head together, as is the case here. So I might expect the actual stiffness’ of the system to be slightly higher than reported here, but only perhaps by 1%.

That we are even talking about errors on the order of 1% is a massive success for this model for combining tripod and head stiffness. Not only do tripods and heads behave very nearly like ideal torsion springs, but their behavior when adding in series is (with the exceptions discussed above) as expected. Given the myriad of approximations and error sensitive formulas we have gone trough get to this point, I consider these results a rousing success for the tripod torsion spring model.

Using this model, the clear next step will be to calculate the optimal head for a given tripod in terms of maximizing stiffness / weight. This has been a long time coming, and I am excited to finally be able to provide a data-backed answer to the question of “Which head should I buy?”

]]>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.

]]>

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.

]]>