Calculating top speed on ice...

[Johansson]

Is there any way of calculating the theoretical speed after 2000m with a given thrust and acceptable aerodynamics? The surface drag will be minimal with metal runners (like long skates) on ice and a glass fibre fairing to keep the air resistace as low as possible.

The engine I had in mind is the Thunderchine with intake augmentors.

Best regards //Anders Johansson

[milisavljevic]

Hej!

Is there any way of calculating the theoretical speed after 2000m with a given thrust and acceptable aerodynamics?

Naturally. . There are several methods available to you, each recommended by the precision
with which certain quantities are known, or may be calculated (modeled). In your specific case,
a pulsejet-powered "kick" accelerating on ice, there are practical limits to precisely calculating
the four (4) critical variables, for any moment in time, or distance from the starting position:

[1] thrust developed
[2] surface friction (drag)
[3] air resistance (drag)
[4] lift (whether positive or negative, lift affects [2] and [3])

This suggests a less rigorous approach (not as computationally intensive) focused on resolving
the ranges (possible values) for each variable, and their various interactions (eg., positive lift
reduces surface friction, but increases air resistance; not to mention adverse control effects).

Fortunately, establishing the boundary conditions for this problem class is straightforward, and
ranges are also established without too much difficulty. While others here may be able to help
you with this, I have solved very similar problems many times over - even as recently as last
week - so I am more than willing and able to help you. The closest match (in my work), was
solving speed over time, and therefore speed over distance, in the case of a pulsejet-powered
pocketbike accelerating on race track pavement. I know I can solve for your 2000 m top speed.

Want some help?

Cheers,
M.

[milisavljevic]

Me again,

I forgot to mention, that ultimately this is a problem that can be solved with a graphing calculator.

No real computer or expensive software required...The best kind of problem to have, in my opinion.

Cheers,
M.

[Johansson]

Want some help?

Hell yeah M!

Just to make things clear, all I need is a rough estimation so I have a clue of what to expect. 10km/h more or less is not relevant at this stage since the actual speed depends on how well I make the aerodynamics on the kick and what style of hat I choose to wear that day.

The handlebars will be 90cm from the ground, the fairing might have to be a bit higher so I can crounch down behind it as much as possible. The distance between the runners will be 55cm or something close to that. I will use a complete flame-proof suit along with my motorcycle clothes so heat or an occational flameout or two shouldn´t be a problem.

[milisavljevic]

Cool!

All I need is a rough estimation... [snip] 10km/h more or less is not relevant at this stage.

Not a problem.

...and what style of hat I choose to wear that day.

Now that complicates things!

Cheers!
M.

[Viv]

Hi Johannson

I would assume this problem is similar to working out the theoretical taxiing speed for an airframe on a runway, if its possible to interchange rolling resistance of tires and bearing friction to ice and runners then you may be able to find a java calculator on a aircraft type web site that will get you in to the ball park.

Viv

[milisavljevic]

Hello Viv!

...similar to working out the theoretical taxiing speed for an airframe on a runway...

But...doesn't Johansson want to know just how =FAST his kick can go in 2000 m, and not how SLOW?!

You know I'm joking with you, right?

If there are online applets for taxiing speed, there must be similar applets for calculating takeoff roll?

The problem in using such an applet is not changing the coefficient of rolling friction to one of sliding
friction, but in the calculation of instantaneous thrust. As a propellor-driven aircraft accelerates, its
thrust is continuously decreasing. Thrust from accelerating turbine powered aircrafts may increase or
decrease, depending on the the engine type and its installation; as this change is small in either case,
we may safely assume such applets treat thrust as a constant. This is not the case with Thunderchine!

If Johansson's Thunderchine is built in spec, with ejectors, net thrust will increase rapidly with speed.
And as we all know of Johansson's fine craftsmanship, we may safely assume that he can build in spec.

Thunderchine's intake splitter, integral ejectors and offset tailpipe are designed to recover energy
from the surrounding turbulent boundary layer. It is a pulsejet optimised for forward motion, and not
static running. In difference to typical aircraft, Johansson's kick will accelerate at an ever-increasing
rate under constant throttle. This is why I offered Thunderchine as a go-kart motor: it is a racing jet!

If I had not [REDACTED] design [REDACTED] it [REDACTED] sustained to the compressibility boundary.*

Cheers,
M.

*ie., approximately 0.7 Mach (230 m/s); not that Anders wants to go anywhere near as =FAST as this!

[Johansson]

Hi Viv and M,

With a good track preparation the sliding resistance will be very low, we moved our 150+kg kick forward with only the slightest push and unlike the resistance of a spiked rubber wheel it should not get higher with speed. The other teams had serious problems with rolling resistance with their ice tyres once they got over 100km/h, cars that had driven over 250km/h on road had problems reaching 200Km/h on the lake due to this added drag. One gocart with +100hp tore one of its rear tyres off somewhere over 120km/h.

That is why I think that runners will be perfect for this competition, paired with a good and lightweight jet engine I don´t think we will make fools of ourselves in the speed competition even against high horsepower cars. It is after all not the acceleration that counts but how fast your vehicle can go without tearing itself to pieces.

[Irvine.J]

1: F=MxA (Add any friction co-efficients here and remember to work in newtons!)
2: Find the displacement in X seconds. s= ut + (1/2at^2)
3: Substitute (or graph) to find the acceleration for the displacement of 2000 meters.
4: You could then use V^2 = U^2 +2as to find your final velocity (V) when you have your displacement and acceleration.
Graphics calculator... bleh i say...bleh!

[milisavljevic]

Hejsan Anders!

We moved our 150+ kg kick forward with only the slightest push...

May I assume the 150 kg included the intrepid pilot? Is it possible for you to break the weight down?
In particular, I would like to eliminate the weight of that gas turbine and any associated equipment.

...paired with a good and lightweight jet engine...

If you build your Thunderchine from thin stainless, eg., 0,5 mm, then it will be lightweight indeed!
The 0,5 mm core pulsejet weighs 2,5 kg; the ejectors "sandbag" your static thrust-to-weight ratio,
but then quickly pay for themselves, "down the road". Or in your case, "down the ice". Ice is cool.

So, Anders...tell me, ah...how fast is "too fast!" ? ...250 kph ? ....300 kph ? .....350 kph ?!

Cheers,
M.

M.'s design tip o' the day: A looong kiiick is better than a short kick, ie., length over the runners.

[Johansson]

May I assume the 150 kg included the intrepid pilot? Is it possible for you to break the weight down?
In particular, I would like to eliminate the weight of that gas turbine and any associated equipment.

Nope, the kick alone was probably 150kg, one heavy bastard built mostly from 10mm thick steel pipes used to line energy drilling holes. I had little to do with the actual building but I helped them with the design and some final adjustments, they built the kick with what they found around the farm basically. Just so you know I will make a new and much lighter kick frame for this engine from thin-walled steel tubing, the other guys will continue developing the turbine kick and race it again next year.

If you build your Thunderchine from thin stainless, eg., 0,5 mm, then it will be lightweight indeed!
The 0,5 mm core pulsejet weighs 2,5 kg; the ejectors "sandbag" your static thrust-to-weight ratio,
but then quickly pay for themselves, "down the road". Or in your case, "down the ice". Ice is cool.

Is there any gain in building the engine from 0.7mm SS instead of 0.5mm? The added weight is acceptable since my 75kg and the fuelling system will be the main source of weight anyway.

So, Anders...tell me, ah...how fast is "too fast!" ? ...250 kph ? ....300 kph ? .....350 kph ?!

Hmm, I guess that if I manage to reach 200km/h I will be more than satisfied. Any faster than that would probably not be very wise since I eventually have to get the darn thing to a halt without getting killed in the process...

M.'s design tip o' the day: A looong kiiick is better than a short kick, ie., length over the runners.

You have a point there, but it has to look similar to the style of kick the average grandma use for her winter walk around the village, otherwise it won´t be a kick I am racing.

As soon as I have started on the engine I will post the progress here, the first engine will be made from 1mm ordinary steel for developements with the fuel injection and thrust measurements, when the design is finished I´ll build three stainless engines. What the other two are for is up to the owner to tell...

[milisavljevic]

Hejsan Anders!

The kick alone was probably 150kg.

Wow! Good to know that this kick will not be the one Thunderchine has to push.

I will make a new and much lighter kick frame for this engine from thin-walled steel tubing.

Cool. When you have it, please post an estimated weight for the kick (ie., frame, fairings only).

Is there any gain in building the engine from 0.7mm SS instead of 0.5mm?

It will be stronger, that's all. Please use whatever thickness that you are comfortable working with.
There's no advantage to the ejectors being any thicker than the thinnest steel sheet you can weld.

My 75kg and the fuelling system will be the main source of weight anyway.

Do you need to carry more fuel than is required for starting and running the 2 km course?

It has to look similar to the style of kick the average grandma use for her winter walk.

We call them "walkers". Now I know what you've been meaning all this time.

I guess that if I manage to reach 200km/h I will be more than satisfied.

Roger! Let's see what we can manage. Hehehe...

What the other two are for is up to the owner to tell...

Oh?! Wow...

Cheers,
M.

[Johansson]

Hi M,

Cool. When you have it, please post an estimated weight for the kick (ie., frame, fairings only).

Do you need to carry more fuel than is required for starting and running the 2 km course?

A "guesstimation" is that the kick frame weighs in at 10kg, the fairings 2-3kg at most, perhaps 5kg for the fuel system and enough fuel to get the engine started and run the track. I´ll try to reduce the weight as much as possible so the thrust-to-weight ratio will be close to or even better than 1.

Roger! Let's see what we can manage. Hehehe...

Great! I have no intention of bragging around with high theoretical speed numbers but it helps to know what performance I can expect to avoid being disappointed (or scared to death with a soiled flamesuit...)

What the other two are for is up to the owner to tell...

Oh?! Wow...

It is nothing secret agent about this, a friend of mine wants to build a jet powered ice yatch (spelling?) to race with next year but since it is his project and since the engine and its fuel system is the main concern at the moment I see no point in discussing it. When the test engine is tuned and running I´ll post some pics of his work if he wants me to, the idea is to keep our profile as low as possible here in Sweden for the Shock-and-Awe effect to work properly at the race...

I don´t think that anyone without previous pulsejet experience can imagine what such an engine sounds like at a close bypass run.

[Irvine.J]

Since you can die at that speed I don't see why your not using the formula I sent which is a piece of piss for anyone with a standard 2 dollar op shop calculator. One or two other formula come to mind and the problem is very simple to work out. 15 minutes and those equations will tell you everything you want to know. In case you forgot falling on hard ice at 200kmh will skin you alive.

Useful equations
F=MxA
s= ut + 1/2at^2
V^2 = U^2 +2as
t= (v-u)/a

Example of frictional force calculation:

A 15kg body on a horizontal surface is subjected to a force of 125N to the right. If the co-efficient of friction between the two surfaces is 0.6 we want to know A- the frictional force, and B the acceleration of the body.
Solution : Fw=mg = 15x9.8 = 147N
first, calulate the weight force as above and, from this obtain the normal reaction Newtons.
Hence, n = 147N
Using Ff= uFn
Ff= 0.6 x 147 = 88.2 N
The resulting force acting to the right Fr is Fr=125-88.2 =36.8 N.This is the unbalanced or resultant force causing the change in motion and using newtons second law of motion: a= F/m = 36.8/15= 2.45m/s^2
Piece of cake, now substitute and do it Johansson and save your skin.

[Viv]

Hi James

That seems pretty easy to follow and work out, just got to plug in the values and off you go, nice to see the art of putting pen to paper and doing it long hand is not lost.

Viv