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As a mathematician and high school math teacher I am, of course, pleased with the correct calculation of the circumference increase. The conversion from metric to English system was equally impressive. Since I still don't understand the physics of pumping I thought I'd point out another variable not yet mentioned.
My Alligator wheels have sidewalls nearly perpendicular to the ground. The O'tangs, on the other hand, have sidewalls with a radiused edge meeting the ground. I wonder if this radius is somehow affecting the grip of the front wheels. A friend of mine showed me his son's ripstik. The wheels look like inline skate wheels with a single one forward and back. After a summer of aggressive use, the rear wheel is flat in the center section, but the front wheel still has a rounded profile. That made me think of the forces affecting the front wheels on my longboard while pumping. A friend who is well versed in physics is going to try and explain why pumping propels you forward as soon as he figures it out. But in the meantime I'm going to experiment with the Alligators. It should be a simple task to radius those corners to match the curve of the O'tangs.
The increase in circumference with the 75mm as opposed to 71mm wheels is around 5%. Again, not understanding the physics involved, this seems like a minor change for such a significant improvement. Yesterday I pumped past a jogger on an incline. This is no 'Big Momma', but before the O'tangs I couldn't pump up that incline at all. As I passed him he stopped in slack-jawed amazement (I was pretty surprised myself) and said "you're going uphill!!" My reply was "Well, it's not much of a hill."
The weather is still holding, so I will continue to experiment and post my results. Here's what I'm going to do. I'll radius two of the Alligators and put them on the front with the standard Alligators on the rear. Then I'll switch and see if there is a difference in pumping ability.
cool, so could you work out a formula?
all this wheel circumference stuff got me thinking
long distance pumping & pushing seems to be 'judged' in the the usual time factor way; cyber miles and marathons etc, or miles covered in 24 hrs.
but as efficiency is really more important, how about some way of measuring that based on 3 variables
Wheel circumference
Number of pumps/pushes
Time taken to complete course
????
am i making sense?
the result would be a number based on the efficiency of the rider
I was thinking of a marathon that was held here in the UK recently, I didn't attend but learnt that everyone had a digital device that logged each personal lap time, now if each rider also wore a pedometer to count pushes or pumps......
be interesting to see the results
I'd bet that the most efficient riders may not come in at the front, but might have the more relaxed and elegant styles?? _________________ Pulse II
Vite BP/Bennet 5'' spherical
+3* wedge & 1/4'' riser
White Khiro barrels
77 mm Vents
RTS 129 rear - 18* neg wedge
maybe the weight of the rider needs to be taken as a variable also?
cant wait to see this formula Surf One, hope it has lots of brackets, numbers, letters and that stuff _________________ Pulse II
Vite BP/Bennet 5'' spherical
+3* wedge & 1/4'' riser
White Khiro barrels
77 mm Vents
RTS 129 rear - 18* neg wedge
I'd bet that the most efficient riders may not come in at the front, but might have the more relaxed and elegant styles??
I like this concept. Finishing a 24-hour distance to me is not only the mileage but the ability to keep on skating, or skate the next day. In other words, to still be feeling as if there may be some reserves, and not to injure yourself doing it. This runs counter to the competitive die-hard stuff I read in bios like Lance Armstrongs or Dean Karnazes. It's more rooted in what guys like Laird Hamilton and the runners in Born to Run book talk about. I think you can still hit competitive times/results this way. My goal's to go for both, as smooth push/pump as possible and hitting personal bests. Now just to plot that on a graph...
On a bit of a tangent, let me address some of the questions youve raised, Surf One.
As for sharp verus rounded lips, yes, a sharp cornerd lip on a wheel is intended to grip more while a rounded wheel lip is intended to slide more predictably. In general, i would stick to hard edged wheels for LDP as sliding isnt something you really want.
As for the physics of pumping, theres a lot going on but ill try to give a brief description. As you roll forward, you gain linear momentum. By turning, you convert some of that linear momentum into angular momentum (a vector). By changing the angle of that vector (turning back the other way) you convert some of the angular momentum back into linear momentum. Thus, by constantly changing the angle of the vector (your angular momentum) left and right, you continually generate linear momentum (which propels you down the path). Thats only half the equation though. The second half has to do with weighting and unweighting the board, thereby converting potential energy to kinetic energy and vice-versa. Ideally, you want the greatest kinetic energy at the point where your change in angular momentum is minimized. That is, when you have reached the farthest point in your left-hand turn and are just begining to turn right, you maximize your kinetic energy to maximize your linear momentum.
Thats probably confusing and im at work right now. Ill try again later but that should give you an idea.
I am really feeling the love here. Usually nobody cares that I'm a math guy.
There are several comments and questions hanging out there I'll try to deal with each one. But first, I must report the results of experiment 127.
At this point it seems likely I will have a Roe Mermaid before I turn 60. But that's still 4 years away and my pumping education must continue. In the interest science, I purchased a Sector 9 Trylam. Since it's a mass produced board it arrived in two days. I put on a similar combination of parts as my Surf One. Bennett Vector 5.0 front, O-W-O bushings, Tracker RTS 129 rear, 17 degrees wedging front, 7 degrees dewedging rear, and 75mm 83a duro O'Tangs all around. Now this is only the second longboard I've ever been on, but it feels like a trampoline compared to my Surf One. Still, it pumps real nicely. It also has this fun, springy feel to it. But I think the Surf One is a better pumper. Here are the questions.
I can't get my foot over the front truck like I can on the Surf One. should I drill new holes and move the truck back? The wheelbase (center to center) of the Trylam is slightly more than 30 inches. The Surf One's wheelbase is 29. Moving the truck back would give my foot more room, and match the wheelbase of the Surf One.
Is this flexy, springy board helping or hurting my pump?
After reading LDPanda's info on wheel lips, I'll can the rounding experiment. But this tweaking thing is sort of addictive. I've also printed your explanation and will soon draw some vectors. My math skills far exceed my physics understanding.
Funkmonk, I can do the math and make you any kind of formula you like. I just have to understand what it is you're trying to calculate first. It seems you are trying to calculate an overall rating rather than just 'who's fastest'. Sounds like a spreadsheet sort of thing. One of the immediate problems is getting the various units in some sort of alignment. You're talking about speed, or time, but related to other variables like weight and efficiency. It can be done. After all, sailboat racing can have a quite complicated handicapping system to figure out who actually won. Is this along the lines of what you want? I'll look at it if you are serious about coming up with something. After all, I owe the people on this forum. I'll tell you why in the next part of this (lengthy) post.
I just got back from skating with someone for the first time ever. I suppose you all already know this, but skating with someone is 10 times more fun than skating alone. I just started longboarding the third week of June this year, so I've got about 3 months of experience, all alone. If not for the help of this forum, I'd be nowhere. Some kid at school (actually, he's a 25 year old teacher) told me he's been trying to pump, with no success, for a couple of years. He's an experienced all purpose longboarder (cruising, carving, sliding) with years of experience. I told him I'd show him what I know. So while the students were working on calculus problems in class today, I put together my new Sector 9. After school, I took him out to the parking lot with the Surf One and the Trylam. I hopped on the Trylam and said 'do this', and started pumping around in circles. He hopped on the Surf One, mimicked me and became an instant pumper!! Within 15 minutes he was kicking my butt. So we swapped boards, and he kicked my butt on the Trylam too. So we raced around the parking lot pumping up inclines, pumping circles, and figure eights. It was a blast. I think he's hooked. So hopefully, when this Roe shows up, I can maybe get even.
Anyway, this has been great fun. Now if I can get some people together to do some distance skating I think I'll have even more fun.
Glad to see youre putting in some serious experimentation, thats what it takes to get your board set up right. The way youve set up the trylam sounds perfect, i cant think of anything i would change offhand. As for redrilling the front truck back a bit, id personally give it some time and work on your technique before drilling holes, but thats your call. A flexy board is good for pumping as long as its the right kind of flexy. If your trylam feels springy and lively, thats good, if it feels soggy and saggy, thats bad. Ive always found the trylam to have a very nice snappy flex (under my 200lbs) so it may just take some adjusting to. A responsive flex will allow you to store potential energy in the board as well as dampen some rough road conditions.
On the math/physics side of things:
Remember that the property which makes a larger wheel roll longer is the same property which makes it difficult to start rolling, inertia. Take that into consideration when choosing wheel size. I would say most people prefer 70-77mm diameter wheels for LDP. Any smaller and you can get tossed by gravel thats usually found on bike paths as well as having a hard time reaching high speeds. Any larger and getting started is a pain and your ideal maintenance speed will be higher and take more energy.
Back to the physics of pumping, since you teach calculus, ill try to come at it from a calculus side. Imagine a vector extending from the front of your board. The angle of that vector would the the angle between where your board is pointing and where you want to be heading. The length of that vector is the linear speed at which you are traveling. Now, imagine that series of vectors through the passage of time as you pump. If you were to sum all those vectors, you would end up with a vector pointing straight down the path which is longer than any one single vector. Thats the first part of the equasion. The second part involves weighting/unweighting. For that, we would take the derivative of our original series of vectors. When we do that, we see that we have two points at which the derivative is pointing straight down the path, those are the two extremes of the turn (farthest left and farthest right). Those are the points at which the change in angular momentum is minimized. If we are to apply maximum energy at those points, we maximize our acceleration down the path. Simmilarly, right before and after those points, the derivative of those vectors point either 'inwards' or "outwards." Thats bad, thats fighting our intent of moving straight down the path. Therefore, we minimize our application of force during that time by unweighting the board.
Hopefully that makes sense. I wish I had an art program that was a little more powerful than MS paint so i could actually draw out these vectors and derivative vectors to illustrate this better. Ill work on that.
Hey thanks for that reply LDPanda. I'm going to draw some pictures tonight and study your vector explanation. It sounds like you know some calculus yourself.
The Trylam feels springy, not soggy. I weigh 175. The Surf One has almost no flex, so no bouncy feel. I'll give the Trylam some more time. I only have about 30 minutes on it, and many, many hours on the Surf One, so naturally, the Surf One feels more familiar. I like the lively feel of the Trylam though. I just got an e-mail that my Roe Mermaid may be coming soon. It will be interesting to feel what an 'optimal' flex is.
I got the Trylam set up so it's pumping well. I dewedged the rear truck to 9 degrees, and installed blue khiro bushings. The front truck is wedged at 20 degrees and uses the orange-white-orange combo. I'm getting used to the springy feel. I think it's more relaxing to ride somehow. I'm not nearly as tired after 8 or 9 miles as I was on the Surf One. But then, I've also learned to pump at different speeds. When I need to accelerate, I use a quick vigorous pump, but once I get over 9 miles per hour I can do this more relaxed sweeping pump that maintains speed. Whenever I drop below 8 mph, I crank up the pumping action until I hit about 9.5 to 10mph, then kick back for a while. I've also noticed that if I get my weight too far over the front truck I really slow down quickly. I'm still not very good on hills, but I'm getting up more of the smaller inclines. Yesterday I had my longest uninterrupted pump at 4 miles. There were a couple of very slight inclines, but an overall drop of 70 feet. My average speed was 9.2 mph. I was pretty happy with that. This morning I went out for a 9 mile ride, mostly pumping. If the weather lasts long enough I might be able to do a 20 miler before winter.
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