Logistic gain on Rotary Knobs

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A typical rotary knob

Rotary knobs nowadays are tangible modalities that have been added to many of our daily lives devices whether it is on our microwaves, our radio or even our hot plates. Just as sliders and other tangible modalities, they are mainly used to parametrize the devices and select specific values and as such sometimes need to be very precise (looking for a specific channel on a radio for example). Being proven to be faster than many other tangible modalities [1,2] and in the pursuit of improving performances like the speed of tasks completion, there have been studies regarding the effects of the size of the knobs, their resistances, the friction, etc...[3] on the performances. But what about logistic gains?

The "logistic gains" that we are talking about is an additional feature which can be added to any modality involving a moving process. It is a feature that is already implemented in many devices nowadays. A common example would be the "scrolling" feature on a mobile phone. While scrolling through documents or a text, it has now become usual to have the scrolling speed increase on the display, the faster you scroll with your finger. And that is thanks to a logistic gain added to the scrolling feature. As this feature has been proven to be quite useful with other modalities, our objective then is to study how well it would do when combined with rotary knobs.



We wanted to do a simple experiment where several test subjects would "play" with knobs on a peculiar task. In order to maximize the amount of feedback we could get from the experiment, we used different sized knobs as well as different logistic gains. Prior to the tests and evaluations, we hypothesized that the most effective knob would be a medium sized one with medium logistic gain. The point thus was to either confirm our hypothesis or reach some other conclusions.


For our study we used an Arduino and a potentiometer to retrieve the rotation values. For the sake of collecting as many of data as we could, we crafted 4 different rotary knobs : 2cm, 5cm, 8cm and 11cm wide and all of them ½ cm high. We also wrote a little program to simulate 3 types of logistic gains for the rotation values, being: static gain, small dynamic gain and high dynamic gain. These gains were function of the rotation distance instead of angle, as a rotation on a small knob means a much smaller distance travelled with the fingers than with a big one. Our study included 12 test subjects of ages ranging from 20 to 68. 10 of them were right handed, while 2 were left handed.

The setup material
The setup connected


By combining all the tools we had in our setup, we obtained a system with the knobs linked to the program we wrote. Our program consists essentially of a horizontal slider-like window with a black background and a tiny red line. Turning the rotary knob moves the red line on the slider according to the rotation.

The experiment was divided in 4 parts: one for each knob. And for each knob the experiment was once more divided in 3 steps: one for each logical gain. For every step the subjects had the same task.

At the beginning our program displays a black background with a small blue area and a red line which represents the current position of the rotary knob. The blue area is a starting point.

The starting area

After the subject has positionned the red line in the starting area, the experiment begins. A relatively wide white area appears at the opposite side of the window. The task is to position the red line anywhere in this area and stay put for a moment. After doing so the target will disappear and another one will appear at the opposite side of the window. The subject then has to reposition the red line in the new target repeatedly until a new starting point appears. This marks the end of that step of the experiment.
For every step, there are 8 targets. The first four are relatively wide targets of constant size, then the last four become more and more smaller.

The first target
The sixth target

At the starting step, the subjects are told to put the red line in the targeted area as fast as possible. The experiment begins when they give the signal that they are ready. Before that, they can move around the red line as much as they want to, to get used to the knob. Additionnaly we didn't keep data about the first two targets each time, as they are considered as training.
The only restriction they have is to keep their hands or fingers on the edges of the knobs and not on the top.

During the experiment we recorded the time the subject took to reach each target. If the subject overshoots, we record when it occurred and how many overshoot there were.


We retrieved the data from the experiments, from which we extracted these first resutlts :

Global performances
Perf by size.png
Perf by gain.png

The first observations we can make from the global performances are :

  • The most efficient knob is the third one (8cm diameter).
  • The high dynamic gain was the fastest to reach the targets.

We expected the first result, as a medium-sized knob should be small enough to be manipulated easily, and large enough to be precise when it comes to smaller targets.
The second result is not more surprising, as a high logicial gain grants higher speeds to reach the targets.

Afterwards, we looked at the proportion of overshoots done by the users :

Proportion of overshoots
Overshoots by size.png
Overshoots by gain.png

We can once again observe two things from the proportion of overshoots :

  • The users did much less overshoots while using the third knob compared to the others.
  • The higher the logicial gain grows, the more overshoots are done by users.

The second result is what we expected, as larger speeds mean less control and precision to stop in time in the targets.
However the second result is surprising. We would expect a -at least- similar result between the third and fourth knobs, as they both theoretically allow the users to be precise when aiming at small targets. Our hypothesis about this result is that as the angular gain is stronger on the 11cm-diameter knob, users had a hard time to accomodate with dynamic gain, therefore leading to frequent overshooting.

We then wanted to see the impact of overshoots on the performances :

Impact of overshoots on performance
Overshoot to perf by size.png
Overshoot to perf by gain.png

We can observe there one of the reasons why overshoots are to be avoided : they increase the time needed to reach and stop in the target, as the total distance travelled by the red line is larger from this extra trip beyond the target.

Another reason is the frustration induced on the user, as shown below.

Users feedback

Once the experiment was over, we asked the subjects which knob they preferred, and what they thought about the different gains. When they had a preference :

  • we counted their answers in an arbitrary scale, counting two points for the size they preferred, one for their second choice.
  • we counted one point for the gain they preferred.

This gave us these results :

User preferences
User preference by size.png
User preference by gain.png

What we observe from these graphs is that they preferred the third knob a lot, which could be explained by the high performances on this knob.
They also highly preferred the small dynamic gain, which seemed to be a great in-between for performances and precision. Additionnaly, they seemed frustrated by the high dynamic gain, probably because it caused a lot of overshoots. However we noticed that despite this, they still preferred it to the static gain, which seemed a lot too slow.

Annex Results

We found extra annex results with our study :

Global performances by Index of Difficulty, the IoD being the target "smallness"

This result shows that our experiment follows the Fitt's law, as we expected. This is not a surprinsing result, but confirms the validity of our experiment.

The impact of rotation direction on performance

We additionnally observed that users were more comfortable while turning the knob towards their hand. This is confirmed by this graph which shows a 12% difference between the two rotation directions.
This result may have to be taken into account in future studies.



On one hand, we saw that the 8cm-diameter knob appeared to be the best amongst the ones we tested. It was overall the greatest in terms of time performances, as well as the one inducing the least overshooting. Additionnally, it is the one that users preferred - which is logical according to the previous results.
On the other hand regarding the logistic gains it was interesting to remark that the high dynamic gain was the most effective performance-wise. However, it was the cause of many overshoots, which can lead in other cases (e.g. with an even greater gain) to time loss. We can state that it is linked with the fact that our subjects didn't like using it that much as they constantly overshooted beyond the target and had to adjust back.

From our study and observations we can conclude that in fact, logistic gains have an important impact on pointing performances with rotary knobs. With our setup the more important the gain, the best performances we obtain. However, from our subjects feedback there is a new parameter we have to take into account which is the "comfort". Appart from one subject, all of them preferred using the 8cm-sized knob with small dynamic gain rather than high dynamic gain.

To go further

A sequel to our study could be to narrow the range of knob size around 8cm and logicial gain values around the small dynamic one. This would precise the results that we got.
An other improvement would be to test on more subjects, as the results are not distinct enough one from another. This would make the study more reliable.
Additionnally, taking into account the rotation direction according to dominant hand can precise the results.
Finally, it would be interesting to increase the dynamic gain to find a threshold at which performances decrease because of larger overshoots.


[1] Simon Voelker, Kjell Ivar Øvergård, Chat Wacharamanotham, and Jan Borchers, Knobology Revisited: A Comparison of User Performance between Tangible and Virtual Rotary Knobs, 2015

[2] Melanie Tory, and Robert Kincaid, Comparing Physical, Overlay, and Touch Screen Parameter Controls, October 2013

[3] James V. Bradley, Optimum Knob Diameter, 1969