How to get the MWR

Hello,

To calculate the PSI (formula 5-7 from the propeller handbook) i have to get the Ad.
And to get the Ad (formula 4-7) i need the MWR. But how do i get the average blade width to calculate the MWR?

And the hub% (from formula 4-7) to get the Ad, if i have a max. hub of 53.4mm and a diameter of 200mm.
do I have to divide the hub diameter by the diameter?
and is the answer in percent?

53.4/200= 0.267
So the answer is 26.7%

 

I'll have to see if I have Gerr's book but....

Normally the:
Area of the disk is A0 and includes the whole disk = (pi/4) *D^2
Expanded area ratio is = (expanded area of all blades, outside the hub/disk area) = Ae/A0
Note that for the B series the nomenclature is number of blades (Z) dot Ae ( i.e. B 3.50)
Developed area ratio (sometimes call the Blade area ratio) = (developed area of all blades, outside the hub/disk area) = Ad/A0
The Mean Width Ratio (MWR) = Mean developed or expanded width of one blade/D = (area of one blade outside the hub/length of one blade outside the hub)/D

Yes, there is a slight difference between Ae and Ad but for MWR the error is small for a B series where the maximum blade width is ~0.6 R.

So we can determine the area of a single blade outside the hub as Ae/Z. The length of a single blade outside the hub is 0.8*D/2. And then the MWR is:
((Ae/Z)/(0.8*D/2))/D

 

Well.....

After a whole day of reading and thinking, I still can't figure it out.
I don't know how find out what the expanded area (Ae) is.
How can I find this out?

 

For a B 3.50, the expanded area of all 3 blades would be 50% of the area of the disk.
The expanded area of a single blade would be 0.5*A0/3
The mean width of a single blade would be it area (0.5*A0/3) divided by the length of the blade, i.e. 80% of the radius of the propeller for a B series.
It's fairly straightforward.

 

So correct me if I am wrong.

But I have a diameter of 7.5 inch.
The Disc area would be (pi/4)*7.5^2 = 44.18 square inches.
The expanded area of all 3 blades would be 22.09.
The mean width of a single blade would (22.09/3)/3= 2,45 inches
Does the mean width mean the same as average mean width?
So the MWR would be 2.45/7.5 = 0,33

 

Yes, while you could develop the actual width of the blade, the idea here is "mean" width. This is the mathematical definition of mean; i.e. "The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count." Since the area of one blade is the sum (width*del R), the number found in the mean.

Edit to add, remember this is for a rounded tip B series...when you start to design high efficiency propellers of much different shapes, you really need to look at cavitation at the specific sections (accounting for actual depth)....but that is very far along in the propeller design process.