Do you, on every climb, conduct an experiment to determine which exact speed provides the best climb rate given current atmospheric conditions and aircraft weight, as opposed to climbing at published Vy?
When the operation calls for it, yes.
Flying jumpers I do it all the time. On a hot summer day, taking a 182 at max gross weight to 11,500 MSL requires the use of a little experimentation. Right after takeoff the published Vy speed works alright. As altitude increases, the airspeed slowly decreases in order to achieve best rate of climb. Towards the top of the climb, if I tried to use published Vy there is no way I'd make it all the way to altitude.
Same for flying my 140. When it's just me and half fuel in the plane, it handles considerably different than at max gross weight. I'd put it on the order of 5 to 10 knots different, depending on what I'm trying to do. It is a small, low-powered aircraft that is very sensitive to differences in weight.
I just started thumbing through my T206H POH, also. Book values can vary considerably based on external factors. In the 206, Va at 3600 pounds is 125 kias. Va at 2300 pounds is 106. Which one should I memorize?
And this brings me to another point that I've noticed with modern aircraft--very few, if any, POHs have a straight table that says, "Vy = x knots," "Vx = x knots," etc. anymore. They have specific speeds listed in their checklists, and have guidelines for speeds to use with their normal operations, but I can't find and new Cessna checklists that actually use the term "Vx" or "Vy" with a specific number attached to it.
However, there is still benefit to memorizing them. It develops a total, overall picture of the airplanes performance envelope and limitations. Having the number in your head reduces the amount of time needed to access it, improving the chances that you will use it properly. If you have to reference the placard that states gear extension speed every time you extend the gear, you are adding extra steps and not displaying the level of mastery I feel pilots should.
I agree.
Also, I don't feel it's very difficult to memorize V-speeds. I have had students kick and scream about memorizing them, and I felt it was nothing other than mental laziness - which is not something I want to support by allowing them to not memorize them.
Fair enough, but it gets a lot tougher to memorize all these random numbers when you're flying multiple aircraft types on a regular basis. I fly a C-140, C-172, C-182, and T206 on a weekly basis, not to mention occasionally ferrying a plane or doing flight reviews or IPCs in other aircraft. I think if I cared that much about memorizing every single V speed for every aircraft I fly, I'd slowly drive myself crazy.
