Mi26 Downwash Velocity

[lucaberco]

Could some kind soul please check my math? I need to calculate an approximate figure for downwash velocity for the Mi26 (!!)

So:

Following the law that Force = (Mass) x (Acceleration), rotor velocity can be expressed:

Downwash Velocity (ft/sec) = √Weight (lbs) ÷ 2 x (air density) x RotorDiskArea (sq. ft.)

In other words, the square root of: the weight of the helicopter divided by two, times Air Density (assume sea level), times Rotor Disk Area in square feet.

In this case, the parameters are:

Weight = 62,170 lbs (empty weight)
Air Density = .002378 slugs/feet cubed (assuming sea level)
Rotor Disk Area = 8,656.8 sq. ft.
Rotor Diameter = 105 ft.

So:

Downwash velocity = √31,085*.002378*8,656.8 = 799.944 feet/sec.

799.944 fps = 545.41 mph.

However, this is at the rotor. Since the air reaches it's greatest velocity 1.5 - 2 rotor diameters below the disk, thus the effective velocity at 210 feet below the rotor disc, the approximate downwash velocity is 1,090 mph.

Do I have this right??

Thank you so much in advance!!

Luca

[the coyote]

Hi there,

I calculate it as:

Disk loading (in lbs per square foot) X 210 and then take the square root.

This gives the average downwash velocity in feet per second.

By my numbers:

Square root(62170 lbs/8656.8 X 210) = 38.8 feet per second downwash velocity, about 2330 fpm.

Bear in mind, you never fly the thing at empty weight, so you need to provide a realistic weight. The heavier it is, the higher the downwash velocity.

[lucaberco]

Hi there Coyote!!

Thanks for taking the time. So if I take the loaded weight of 109,350 lbs, per your calculations, it would look something like this:

√109,350÷8,656.8 x 210 = 51.50 fps, or 3,090 fpm, or 35.11 mph.

A.) Did I do your math correctly, and
B.) Does this sound right for the Mi26?

Thank you!!

[the coyote]

A: Math is good
B: No idea, sorry!!

By my numbers a Bell 412 at 11900 lbs gross weight and rotor diamter of 46 feet will have a downwash velocity of 38.8 fps or 2330 fpm.

An S76 at 11700 lbs and rotor diameter of 44 feet will have a downwash velocity of 40.2 fps or 2412 fpm.

3090 fpm seems high to me, but I am no guru by any means, just a line pilot.

By the way, the math was given to me by Nick Lappos, I presume it will vary with air density quite considerably. My interest in it was largely to calculate risky rates of descent that might make you catch that downwash and put you in VRS territory.

Cheers, coyote.

[lucaberco]

Thanks, Coyote!

One final go-over; because I think it's making sense.

√(Weight÷Rotor Diameter) x (Rotor Diameter x 2)

Is this correct? I'm assuming the 210 figure that you used was the Mi26 rotor diameter times two, correct?

And it's Weight ÷ Rotor Diameter, NOT Rotor Disc Area. Would that be correct?

Thanks again, Coyote!!

Best,

Luca

[dClbydalpha]

Hi, I hope that this clarifies the maths.

The velocity induced at the rotor is

Vi = SQRT((Thrust)/(Disc Area * 2 * airdensity))

(Sorry I can't get a formula editor to work ...)

Thrust/Disc Area is the same as disc loading so

Vi = SQRT (discloading/(2*airdensity))

standard air density is 0.002378 slug/ft3

(1/standard air density) is 420.5 which, when divide by the 2 is where the 210 factor comes into the equation. This is the bit that would change for different air densities. Take the invert of the air density and divide by 2.

This gives the induced velocity at the rotor, as you already pointed out lucaberco, the velocity downstream increases.

[WillDAQ]

I didn't know PPrune did people's homework for them

I'd suggest that 1,090 mph is wrong.

[lucaberco]

Thanks, WillDAQ!

Just FYI, the application is a major motion picture. One of the big action sequences involves an Mi26. Asking this question is due diligence for all the obvious safety reasons, but also for SFX and the Art Department as the legendary downwash from the Mi26 could have some serious construction implications.

So if you think that 1,090mph is high - and I do too, then maybe you could help steer me in the right direction.

Cheers,

Luca

[dClbydalpha]

Just to add why your initial calculation came out with 1090mph

The formula you gave is
Downwash Velocity (ft/sec) = √Weight (lbs) ÷ 2 x (air density) x RotorDiskArea (sq. ft.)


Whereas you calculated
√31,085*.002378*8,656.8

If you calculate

√31,085 ÷(.002378*8,656.8) you get 38.8 ft/s as The Coyote established earlier. So you're science was right ...
As you also said, in ideal flow the veloctiy will double by the time it gets out of the rotor influence which you need to consider.

I'm sorry I don't have any Mi26 specific data but typical induced velocities for a range of helicopters are between 30 and 65 ft/s.

If you are using this data to carry out any safety related calculations then I would suggest you need much more than the physics used above. These are free stream type approximations. As soon as you get near the ground it gets very different. It's not just a case of the velocity of the air but also the sheer amount of air that is being moved that causes problems ... when close to the ground this all has to go somewhere.

[SilsoeSid]

Why not ask an operator to get someone to stand underneath one with an anomon, enomin, ominon, anemometer ?


Surely if at's a fast as 1,000 mph the guys wouldn't be able to be under there, let alone the nearby tents!

Mil Mi-26 Halo Sling Loads CH-47 - YouTube


...or cameraman :ok:

http://www.youtube.com/watch?v=268B_VXQ-Kw

[lucaberco]

Thanks, dClbydalpha!!

:D

[spheritech]

The formula is: downwash= 2*sqrt{gross weight*g/{2*density*rotor surface}} 2 times the theoretical induced velocity

For your example
-gross weight =28200 kg
-g=9,81m/s2
-density=1 (ISA sea level)
-rotor surface= 804 m2

Downwash velocity= 26,2 m/s (86 ft/s or 51 kt)

Cheers,

[dangermouse]

as 1090 mph is about mach 1.3!!!
DM:ooh:

[[email protected]]

Spheritech, why have you used 1 as air density at SL when it is 1.23 kg/m3?

Surely when considering the effect of downwash on objects on the ground it is better to ignore the free stream speed and just use the induced velocity ie half your equation's answer?

[Decredenza]

I have never been around a 26 so I haven't a clue. One thing that I noticed from the equations was the use of the entire rotor area. I thought only the outside third was used for lift and therefore creates downwash...

http://i385.photobucket.com/albums/oo293/snippet58/rotor.png

Driven (lift) Driving (autorotation)

I just tell people it is as windy as standing up in a convertible car driving at highway speeds.

[the coyote]

Decredenza,

Your basic picture is for autorotation, not powered flight.

The entire rotor disc area is used because that is what determines the disc loading. Lift is produced by changing the momentum of air, and the higher the disc loading, the greater the momentum change required, and thus a greater resultant downwash velocity.

[AnFI]

Just to cross check:

Surely:
( rate of ) Momentum change (see Newton's Laws) gives the same thrust whether it's a high disc loading or a small one..... the difference being that with the smaller area of a high disc loading a greater flow rate is required (since the area is small a taller column of air is required to move per time to acheive the same momentum change - ie a greater Ind Flow)

The greater Ind Flow with a smaller disc (higher disc loading) just requires more POWER ....
?

[spheritech]

Crab,
My mistake for air density which is 1,225 kg/m3 as you pointed out.
Concerning the use of induced velocity insted of free stream velocity I believe the truth is somewere in between. It depends of hover height.
To know the truth, we have to use SilsoeSid method.:)

[Decredenza]

Not a 26 but gives an idea...

http://www.youtube.com/watch?v=-X_eB_gUFkw