The Futility Of Benchmarking Mice
The fact that none of the mice failed our testing was interesting, and it compelled us to conduct yet another set of evaluations. First, we checked for the manufacturer-reported tolerances of each mouse, namely their top movement speed. Razer's Orochi, for example, is rated for the lowest speed at 100 inches/second, and yet even that seemed unnecessarily high to us (particularly given the size of a typical desk). Obviously, you're not going to drag your mouse across your entire desk, and especially not in one second.
So, in order to overwhelm the Orochi, you’d need to drag it across a 10-inch mouse pad, pick it up, move it back to the starting position, and drag it across nine more times, all in the span of a second. In other words, regular movement inside the boundaries of a mouse pad could never exceed the maximum speed rating of these devices.
With this in mind, we wanted to determine the maximum speed of an average person’s wrist movements. To do so, we set up two switches ten inches apart. We then had a subject rapidly activate both switches. The activation time was recorded, and we subtracted the first switch’s activation time from the second, arriving at an approximation of the time it takes to traverse our mouse pad.
The average activation time of the second switch was around 92 ms, with a standard deviation of three. The total measured time was between 243 and 268 ms. Using the lowest recorded value, the maximum recorded speed over 10 inches was around 49 inches/second. This means that there is a huge difference between the speed an average person can move his or her wrist and what a third-gen laser sensor can reliably pick up, record, process, and transmit.
Under normal operation, we're exceedingly confident that you won't approach the tolerances of these devices. You're just not fast enough to cause them to fail. Sure, we're taking a big leap by calling our test subject average. But you'd have to move two times faster to even touch Razer's rating.
Acceleration, the rate at which the velocity of an object changes, is closely linked to speed, and therefore, to DPI. Given that there were no inconsistencies in the output of any of these mice during our speed tests, we can also conclude that they had no issues with acceleration. Still, we wanted to crunch the numbers and figure out why.
To begin, the Razer and Logitech devices are rated for up to 30 G (gravitational constant) of acceleration, and while I couldn’t find any data for Thermaltake’s submission, this doesn't really matter, either. It's important that you understand just how ludicrously high 30 G is. That’s the pull of a planet 30 times as massive as Earth. If you were subjected to that, you would immediately lose consciousness. If you were to free fall at that rate, you would be traveling at over 650 miles per hour within one second. Achieving this kind of force in daily life is utterly unfathomable.
With that in mind, we can start looking at what kind of acceleration that would be realistically encountered. The most basic formula for acceleration is as follows:
Where a is acceleration, delta v represents the change in velocity, and delta t represents the change in time. Using the numbers we collected earlier, we’re able to figure out that over the course of about 0.15 seconds, the human wrist can consistently achieve an average velocity of 49.6 inches per second. That works out to 1.26 meters per second over 0.15 seconds, or less than 1 G. Again, we should be fair and state that we used average velocity and, as a result the figure we see is an average acceleration. But, it does beg the question, what would 30 G really mean for a mouse?
Working the equation backwards, beginning with acceleration:
=294 m/s2 * 0.15 s
We’d need to have held an average velocity of over 1,736 inches per second to reach the limits of the device. That’s over 17 times the maximum speed that the Orochi can handle, giving us a pretty clear understanding of how and why our measured acceleration is so low. It is, of course, to be expected that, at some point in those 151 milliseconds, the acceleration of the mouse was greater than 1 G, but if it had hit anywhere near 30, one or more of the mice would have failed our velocity test.
At the 1 ms reports per second these mice make, it is unreasonable to think that they would ever have any serious problems. Modern laser imaging is too fast, and the human body is far too slow to hit those limits without causing serious damage to the mouse itself.
Understanding what it takes to make these things fail, and the fact that they haven't, certainly gives us an enormous amount of respect for the engineering behind today's mouse technology.