Hi Guys,
I'm currently doing my first electric conversion of a glow plane and as many of you know, electric motors unlike their glow counterparts need a down and left thrust angle (around 2deg) to work properly.
This did kind of yield a simple yet interesting problem - if you get a rigid metal motor mount which doesn't have the thrust angle built in you will have to mount the whole metal motor mount at an angle.
Now with electric conversions motor mount will be quite long so this means you will have to offset the whole motor mount in order for the shaft to come out in the middle!
Now I'm not a person that likes to do it based 'on the feel and looks' - I'd rather properly calculate the offsets and number of spacers I need to put in (I'm an math whore!)
There is plenty of engineers here so they might share an better approach - anyways - my motor mount is a bit funky in a sense it's not square based (rectangle) and that the motor is not mounted in the smack middle but on the upper (picture attached).
The approach presented here can be generalized to any kind of firewall (starfish, pentagram, circle, euclidean geometry of Cthluhu stronghold)
The idea is - we measure (in this case) 5 points of interests of the firewall - 4 base points where the screws come in and the point where the shaft should come out of the cowling.
With those 5 points we construct a simple mesh within 3d euclidean space which we then transform with two rotational matrices around the X and Y axis.
This yields new point coordinates - and voila - we got X, Y offsets for the whole motor mount and thinness of spacers we need to put in 3 of the base screws to get the thrust angles right.
So:
step 1) - measure the motor mount (between the screws):
In my case
- width wise the base screws are 80mm apart
- height wise the base screws 60mm apart
- the shaft from base to where it comes out of the firewall is 130mm deep
- the center section of the motor shaft from the top screws is 14.5mm apart (as mention and seen on picture - it's not central)
step 2) - create the mesh
In this case it's just going to be 5 points.
Because we are rotating around the base points will be at the Z = 0 depth.
Because we want the offset of the center piece the point on the shaft will be at (X,Y) = (0,0)
So in my case we have the following (X, Y, Z) coordinates:
P1 - upper left corner of the motor mount
P1 = (-40, 14.5, 0)
P2 - upper right corner of the motor mount
P2 = (40, 14.5, 0)
P3 - lower right corner of the motor mount
P3 = (40, -45.5, 0)
P4 - lower left corner of the motor mount
P4 = (-40, -45.5, 0)
P5 - point on the shaft where the whole thing is coming out
P5 = (0, 0, 130)
As seen on screen (I'm bad with pictures sorry):
Now let's rotate this little construct to get the right thrust angle - first rotate it right around Y axis with Alpha degrees to get the right thrust angle and then against the X axis with Beta degrees to get the down thrust angle.
(The formulas here are for counter-clockwise rotation).
So a bit math here:
The transformation rotation matrix around Axis Y (Ry) and X (Rx) have the following formulas.
In order to get the transformation matrix for rotation against Y axis first (for left thrust) and then X axis (for down thrust) we multiple Matrix Ry by matrix Ry and get the following product (keep in mind Ry * Rx is different from Rx * Ry)
To get the coordinates of the new point we multiple the old coordinates by the transformation matrix (formula bellow):
So let's put some numbers in (because now it's easy)
I'm going for standard 2 deg down and left thrust (So both Alpha and Beta are 2 deg)
sin(2deg) = 0.034899497
cos(2deg) = 0.999390827
So the formula roughly looks like:
Now putting in the numbers I get
P1 = (-40, 14.5, 0)
P1' = (-39.95, 14.49, 1.9)
P2 = (40, 14.5, 0)
P2' = (39.99, 14.49, -0.89)
P3 = (40, -45.5, 0)
P3' = (39.92, -45.57, -2.98)
P4 = (-40, -45.5, 0)
P4' = (-40.03, -45.47, -0.019)
P5 = (0, 0, 130)
P5' = (4.53, -4.53, 129.84)
Rounded it up to two digits.
Ok so those are nice numbers but what do they tell us?
The important one is P5 - it tells us that after applying the 2 deg down and 2 deg left thrust the point will move by 4.53mm left and 4.53mm down from the original location:
This means that I have to offset the whole motor mount by 4.53mm to the top and 4.53mm to the left in order for the shaft to still come out of the middle of the cowling.
Another important information is how many spacers I need to add to each of the point on the mount to get the 2 deg left and 2 deg down downthrust!.
If we look at the P3 which is the 'lowest one' - if we treat it as a zero (touching the firewall)
It means that:
- on the upper left corner (P1) I need to add 4.88mm of spacers (1.9mm + 2.98mm)
- on the upper right corner (P2) I need to add 2.09mm of spacers (-0.89mm + 2.98mm)
- on the lower left corner (P4) I need to add 2.961mm of spacers (-0.019mm + 2.98mm)
Hope this helps someone
OK - mistake on my side - it should be right side thrust so it should be Ry(-2deg) not Ry(2deg) - case is symmetric so no problems there but will amend!