Lower Maffs - silly puzzles for the winter

Canadian Paddler · Post by **Canadian Paddler** » Thu Dec 08, 2005 1:39 pm

It seems that our excursions into lower maffs, and general weird assumptions have upset others on the gate width thread, so here are a couple of questions to think about:

Given an 'idealised 'slalom course of 500m through the gates,
idealised water, where the paddle does not slip at all
a winners time of 100.00 seconds:

a) what is the maximum and minimum average speed of the tip of a paddle blade and why?
b) what is the average cadence (strokes per minute) of the winner, NB I measure cadence as strokes on one side, so left right is 1, not 2.

I have ideas and assumptions, but will let the other lower mafmatitoans jhave a go/flight of fancy first

Enjoy!!

Pingu · Post by **Pingu** » Thu Dec 08, 2005 5:53 pm

I don't think that I really understand the question.

However if the boat has gone 500m in 100 seconds then it has travelled at an average speed of 18 km per hour. (0.5 x 3,600/100)

... If the boat has travelled at that speed, then presumably the paddler (and the paddle) have all travelled at the same average speed as well?

???

Kev.S · Post by **Kev.S** » Thu Dec 08, 2005 8:46 pm

Keh!! where does that leave a super speedy C1 paddler such as yourself CP, or even worse me in a C2?

Up the proverbial creek I suppose.

Canadian Paddler · Post by **Canadian Paddler** » Fri Dec 09, 2005 8:32 am

Ah glashopper! the simple answers eh? but the paddle TIP does not go in a staright line, it moves in an arc so travels further than the boat!, so we can get into how much of an arc, and how many strokes (leads on to cadence question!)

Then we get onto maximum and minimum because if the pattern starts with the right battle at front of the boat and ends with the right paddle at the front of the boat paddled it cover the same distance. BUT if they start on a right hand stroke and end on a left hand stroke, has the paddel tip travelled the same distance?

:p

Pingu · Post by **Pingu** » Fri Dec 09, 2005 8:51 am

I'll get my coat!!!

C1DAD · Post by **C1DAD** » Fri Dec 09, 2005 2:12 pm

28.928 KM/HR MIN
29.06 KM/HR MAX
75.42 CADENCE.

There are so many variables in this, that the above is almost certainly wrong!

C1DAD

???

Canadian Paddler · Post by **Canadian Paddler** » Fri Dec 09, 2005 4:26 pm

75 strokes a minute!!!! good grief, no wonder I do not win! What assumptions do you make to get there? :0

C1DAD · Post by **C1DAD** » Fri Dec 09, 2005 5:02 pm

At the risk of appearing any more of an Anorak (or possibly as a reflection of the amount of work I have on at the moment!), assumptions as follows:

We are talking about K1

The power cycle (Blade in the water, assuming it starts and finishes the instant the blade enters/leaves the water) describes a chord length of 1989mm, with the versed sine being 480mm (This is equivalent to the length of the blade, in this instance 480mm, being fully immersed at the 6 o'clock position of the stroke).
The radius of the arc is 1270mm (This all varies as the o/a length of the paddle, in this instance 2040mm, and the grip width, in this instance 500mm) But the 1270 radius is based on the top hand being the centre of rotation.

From there, its a basic sum of distance travelled divided by chord length per stroke to give total number of strokes (sum of left and right hand strokes). This then divided by 2 to give the number of stroke 'cycles'.

Then Adjusted to cadence.

My thesis on this will be published shortly with diagrams..... ooh dear i've come over all faint, I must go and lie down now.

C1DAD

:;): :;): :;):

John Sturgess · Post by **John Sturgess** » Sat Dec 10, 2005 1:21 am

I don't understand this maths bit - I thought your sines were the bits at the back of your nose that get sore when you have a heavy cold - but the top 5 paddlers on their final runs at the BStM Worlds took on average 94 secs to get down, and took on average 102 forward strokes (power and sweep) 2 backward sweeps, and 8 bow-rudders to do so

Bus Driver · Post by **Bus Driver** » Sun Jan 08, 2006 7:00 pm

Colin you obviously have far too much time on your hands,

does the paddle length and the blade area make any difference to your calculations?

... longer shaft would I thought mean that the distance that the blade travels during a cadence is further than if someone has a shorter shaft?

...that is not a personal attack on people with either longer or shorter shafts, ie it is not shaftist

Canadian Paddler · Post by **Canadian Paddler** » Mon Jan 09, 2006 9:50 am

Shafts - sounds like you know about that, it surley does not depend on construction, colour, or glitter!

Hey I have not poseted here for a while, as I am far too busy getting over being one sided, and no I do not mean C1 or C2!

expletive deleted C1DAD managed most of the assumptions I was hoping to look anoraky picking people up on!

The disparity between World Champs and our theoretical water is relatively easy, the answer did not take into account water flow - and there is a bit of that on a WC course!

Anyone with still too much time can have a go with assumptions about water speed, and how much of teh course is in breakouts, where the water sped is lower, although still through the gate, if really bored make an assumption about paddling against teh current as well! :rock:

C1DAD · Post by **C1DAD** » Tue Jan 17, 2006 11:03 am

I,ll take that as a complement CP.

Taffi · Post by **Taffi** » Wed Jan 18, 2006 5:06 pm

You sad people havnt you got anythink better to do!