Calculating top speed on ice...

[milisavljevic]

Hejsan Anders!

No time for any night runs for a couple of weeks, on thursday I go on a 3 week vacation.

Too bad, so sad.

About the throttle valve, the needle is ground so the fuel flow is roughly linear.

Very sweet, considering you were working with a circular port. It takes a slot to achieve true linearisation.

Cheers,
M.

PS: Have a great vacation!

[Johansson]

For a true night run I´ll have to wait a month or two since it never gets dark around here in the summer, I don´t want to run it at midnight either since my guess is that I bother people enough with it at daytime...

Yes, it took a while to get the fuel flow that linear. The "bump" just where the non-return valve opens couldn´t be modified away for some reason, but I don´t think it will be noticable.

[milisavljevic]

Hej!

For a true night run I'll have to wait a month or two...

No worries. The big idea is to have more contrast to pull out the heat pattern (think: overexposure).

It took a while to get the fuel flow that linear.

What you did achieve is more than acceptable. That "bump" is not something that you can eliminate,
or rather, it would never be worth the trouble and expense to reduce it. The graph is most excellent.

Cheers,
M.

[Johansson]

I had nothing to do after work today so I searched the scrap bin and found enough material to build the battery and throttle wire mount, so this wednesday was not completely wasted after all.

I also bought handlebars grips and a brake lever to use for throttling, by coincidence the diameter of the frame turned out to be the same as a bicycle handlebar (22mm) so it fitted liiiike ei gluuuuve!

[milisavljevic]

Hejsan Anders!

Totally awesome, dude!

Today, I bought the Compleat Illustrated Guide to Thumb Twiddling (2009);
should help me piss away time whilst you are on vacation. Once can only hope!

Cheers,
M.

[Johansson]

(...)should help me piss away time whilst you are on vacation.(...)

That I cannot allow!

I´ve just been down and checked the weight of the kick. As it stands in the most recent pics it weighs in at 29kg, not including the wooden (yes it will most likely catch fire) seat, one gallon of fuel, ejectors and some wiring and fuel lines. Lets say 35kg ready to go, add my 85kg (protective clothing included) and you get a total weight of 120kg.

While I am away you can work your magic on the calculator and figure out a theoretical top speed after 2000m, since this thread is called "Calculating top speed on ice" it would be a shame if we didn´t post any speed guesses in it...

[milisavljevic]

Hejsan Anders!

That I cannot allow!

LOL...I was "kinda sorta" looking forward to your vacation, as I need to focus on some other tasks for a time.

It would be a shame if we didn´t post any speed guesses in it. [this thread]

No rest for the wicked! No worries there; however, the calculations may not be completed while you are away.

I've just been down and checked the weight of the kick...one gallon of fuel...and you get a total weight of 120kg.

Hmmm...one (1) gallon of E85 is not going to last. Under ideal circumstances, this may be more than enough;
however it would be wise to carry more fuel than needed. I will have a think on this while you are on vacation.

Now be gone with you! Don't do anything I wouldn't do. On second thought, please do: you will have more fun!

Cheers,
M.

[Johansson]

Hmmm...one (1) gallon of E85 is not going to last. Under ideal circumstances, this may be more than enough;(...)

I know that it will be a close call, the idea is to refuel once the engine is started and running on liquid. A two gallon tank would have been better but it would also have taken up all space in front of the engine. After I get back from the vacation I will finish the fuel system and try to get the engine running on E85, if everything goes as planned I will find out how long the engine can run at full throttle on a gallon of fuel.

Now be gone with you! Don't do anything I wouldn't do. On second thought, please do: you will have more fun!

Count on it!

[milisavljevic]

Hej!

The idea is to refuel once the engine is started and running on liquid.

Roger. Topping off once started sounds smart and it is certainly volume efficient, IF you can do it safely.

Enjoy your vacation and let's catch up on the flip side!

Cheers,
M.

[Johansson]

Roger. Topping off once started sounds smart and it is certainly volume efficient, IF you can do it safely.

The safety issue is the main reason why I would prefer diesel as the fuel of choice, if a leak is sprung it is less likely that the entire kick would go up in flames with diesel compared to gasoline or E85.

[tufty]

My guess as to top speed follows. Thunderchine is, I believe, a nominally 55lb motor, so let's assume that. You can plug in other figures later if needed.

First off, convert to newtons. 55lb ≈ 244N

Newton tells us that Force = Mass x Acceleration

Assuming zero drag, we could simply plug that in and get the acceleration, and thus the speed at any given distance travelled. This might give us a useful upper bound, but it's going to be "optimistic". So, we need to look at drag and friction.

First off, aerodynamic drag.

Let's assume the kick has a drag coefficient similar to that of a bicycle or a skier, or around 1.0. This handily gives us a drag force of ½ρv²A, where ρ is the volumetric mass density of air, and A is the frontal area of the kick. Assuming a temperature between ±10C on the lake, we can estimate ρ at around 1.3. At a guess, the frontal area of the kick is around 0.5m²

So, at any given time, the aerodynamic drag force is going to be of the order of 0.325v², where v is the velocity in m/s relative to the medium (we'll assume still air for simplicity)

Next up, frictional losses.

Steel on ice has a very low coefficient of friction, somewhere between 0.004 (for special speed skates) and 0.1. We'll assume 0.01, as a relatively reasonable figure scientifically plucked from my arse (and based on the fact the ice is unikely to be mirror-smooth)
The kick itself will be running horizontally, so the normal force is simply the weight of the kick + rider * g, or 1177N, giving a frictional force of 11N or so regardless of speed.

We'll ignore the static friction by assuming that the thrust of thunderchine is enough to overcome this. If it's not, you're fucked, but you'll melt a nice pool of water while you're trying to get going.

So, what does this give us?

Well, the driving force, Ft, at all times will be F(thunderchine) - F(friction), or 233N
The aerodynamic drag force, Fd, at a given instant, will be 0.325v²
The acceleration, A, at any given moment is therefore (Ft - Fd) / 120, or (233 - 0.325v²) / 120
Velocity, v, at any given time t is the integral from 0 to t of A.
Distance travelled, x, at any given time, is the integral from 0 to t of v.

Rather than buggering about integrating all this twice and then back solving for x = 2000, which I was never any good at even when I could remember how to do it, let's write some code.

Code: Select all

#!/usr/bin/ruby

x = 0.0
v = 0.0
t = 0.0
a = 0.0
dt = 0.001

# calculate until we get to the magic 2000m mark
while x < 2000
  t += dt
  a = (233.0 - (0.325 * v * v)) / 120.0
  x += v * dt
  v += a * dt
end

puts "t = #{t}s, x = #{x}m, v = #{v}m/s, a = #{a}m/s^2"

Which gives me this result

Code: Select all

t = 84.2540000000382s, x = 2000.00155627203m, v = 26.7751553335021m/s, a = 3.82845668307634e-05m/s^2

Obviously, the reult varies depending on the choice of dt, but the orders of magnitude are the same even if we go down to the scale of seconds rather than thousandths.

27m/s is 97km/h or about 60mph.

[edit] It occurs to me that the rated 55lbf is "sans ejectors", and that their performance will vary depending on forward speed. Any estimate as to how much they will add, m?

[Johansson]

Holy crapamoly, this calculation would have taken me longer time than the build has so far...

97km/h was a bit slower than I had expected, but since I stubbornly refuse to use fairings on the kick I will have to accept high aerodynamical drag. Even if I can get the drag down some by bending the old knees a bit it would be difficult to reach speeds around 150km/h, given that the calculations are correct. Damn...

[ace_fedde]

Johansson,

Reduce weight! Start with the battery and, no beer on the holidays

Fedde

[Fricke]

the idea is to refuel once the engine is started and running on liquid.

Why not use a external fuel supply until your ready to run the race track?

[Johansson]

Why not use a external fuel supply until your ready to run the race track?

That could work, but the transition between the external tank and the on board fuel cell might kill the engine. Easier just to top it off from a bottle.

Reduce weight! Start with the battery and, no beer on the holidays

Without a battery I won´t go very far, about as far as I can push it.

I am actually very satisfied with the weight of the kick, I cannot think of anything on it that can be removed or made lighter without building the frame out of aluminum. As for myself I am pretty skinny (184cm, 76kg) so no big savings to make here either. If I weren´t hung like a horse I might have saved 5kg, but one can only dream...