maths/blade tip speed question

[Balders]

OK, so I should have concentrated more in maths, but just chatting to a mate at work and was talking about sub-standard blades and said you don't want to have the blade fly off at....errrrr......speed!

So I'm guessing, say to calculate the speed that the tip of a blade is travelling at, you'll need something like:

2 pi r to calculate circumferance
rpm x circumferance to work out distance per minute?
convert that to km's per hour and then miles per hour?

I ended up with 432000kph which is obviously a big mistake

EDIT - just realised, I didn't convert mm to m so I've ended up around 432kph or 268mph which is a bit more realistic, but damn scary!

Am I along the right lines?

So something like a 450 running 325mm blades (plus say 3cm for the head) running at 3500rpm would give what? Just roughly

I know I should be able to work this out myself

[xygax]

ok, so i should have concentrated more in maths, but just chatting to a mate at work and was talking about sub-standard blades and said you don't want to have the blade fly off at....errrrr......speed!

So i'm guessing, say to calculate the speed that the tip of a blade is travelling at, you'll need something like:

2 pi r to calculate circumferance
rpm x circumferance to work out distance per minute?
Convert that to km's per hour and then miles per hour?

I ended up with 432000kph which is obviously a big mistake

edit - just realised, i didn't convert mm to m so i've ended up around 432kph which is a bit more realistic, but damn scary!

Am i along the right lines?

So something like a 450 running 325mm blades (plus say 3cm for the head) running at 3500rpm would give what? Just roughly

i know i should be able to work this out myself

(2*3.14*(.325+.03)*3500)/60 = m / s = 130.04

so M/s to KMH = *60*60 /1000 or 468 KmH



s

[rachel]

wow do you like sitting in a cupboard eating pot noodle ?????????????

This is propper boffin stuff !!!!!

All I know is dont go near a spinning blade lol

[Balders]

haha Rach, I know, it was just one of those moments where you are chatting about a subject you are comfortable with, and then suddenly get stumped.

Interesting though, especially if you've ever been hit...ask me how I know!

[steve_b]

Just worked this out for the 690s on my 90 helis and it comes out at 580 Km/hr, and when you consider that these things weigh around 200 grams that's a reasonable amount of energy to get rid of. When I've been caught on the shins during a spool down then it smarts, imagine one hitting you at full pelt

[Steve]

Here you go:



Pi = 3.14159
HS = Head Speed in Revs/min
BL = Single Blade Length in mm
HW = Head Width = distance between the centres of the blade bolts in mm

So, if head speed = 2000 rpm, blade length = 600 mm and head width = 120 mm for instance,

the tip speed is 497.6 km/h



Edit: If you want it in mph, then multiply the answer by 0.62137119 = 309 mph

[Steve]

All we've calculated here is tip speed, which is the maximum speed of the blade in a straight line. The actual speed decreases as you move in from the tip towards the centre. Also, momentum is a product of speed and mass, and the mass is spread along the length of the blade and is not all concentrated at the tip, so calculating the energy carried by a whole blade is for example it broke away at the root is complicated equation with two non-constant variables (three if you include wind resistance), which will (I guess) require an integrated solution.

[Steve]

This might help too:

[Snaaakeey]

Steve ! You are a super nerd! well done !

According to your sheet My tips on the 6hv are doing 350mph!

[gazza131]

l Agree with Rachel... dont go near em "

[Snaaakeey]

One of the test pilots for the 7hv is running 2500rpn on 700 blades! thats.......

[Snaaakeey]

One of the test pilots for the 7hv is running 2500rpn on 700 blades! thats.......

445 mph !!! 2/3 of the way to the sound barrier!

[Balders]

thanks all, been quite an interesting trip down mathematical memory lane

[Steve]

Just to Compare with approximate head widths:

450 Size heli, 325mm blades, 60mm centres, 3000 rpm = 250 mph
30 Size Shuttle, 550mm blades, 100mm centres 1500 rpm = 210 mph
55 Size Heli, 620mm blades, 120mm centres, 2100 rpm = 335 mph
90 size, 710mm blades, 140mm centres, 1950 rpm = 360 mph

[Rotorhead]

Considering that the tip is going to be the first part of the blade to hit you if you fly into yourself or someone else, 400mph and up is nothing to underestimate, at that sort of speed they dont need to have a sharp edge......