Twisted wings cutting

You were numerous to appreciate the automatic machine to cut out polystyrene. I propose here a system to cut out the tapered twisted wings of your foamies.

If the cutting machine makes it possible to cut out properly a frayed wing, the business becomes harder in the case of tapered wings. The arc shifts transversely, the strings slip along the wire, in short it is not the foot...

If the wing is not twisted, there is always the solution of the fixed point method, but with a twisted wing or from which the profiles of salmon and root are different, it becomes difficult...

 

• the principle:

  Let us suppose that our profile is perfectly flat, if there were no twist one would have a beautiful paper sheet, a plan. The twist consists in raising the trailing edge of our plane profile at the level of salmon to obtain a kind of propeller. One can then notice that the shift in height induced by the twist increases linearly from 0 at the leading edge until the maximum at the trailing edge.

  Let us take again a standard profile now (not flat...) the same reasoning applies to the airfoil chord: the shift in height induced by the twist at the level of the airfoil chord, increases linearly from 0 at the leading edge up to the maximum at the trailing edge.

  If one projects the lines formed by the leading edge and the trailing edge, one obtains two lines which intersect in a point (that I name " fixed point "). It is the point of intersection of leading and trailing edges of the same wing but without twist.

  For a wing without twist, one would use only one gauge and the method of the fixed point. Since one wants to twist the wing, it is enough to find a method to make " move up " the fixed point as one moves from leading edge towards the trailing edge of the profile.

   

• how to make " move up " the fixed point?

  Nothing simpler, it is necessary to hang the " fixed point " on a slide of drawer placed vertically to leave only one degree of freedom verticaly. (in blue on the diagram).

  The fixed point is consisted a 3 mm diameter kneecap of.(brown on the diagram)

  The fixed point will be able to go up while following the twist imposed by the selected profiles. (It is necessary, of course to have 2 gauges, at each end)

   

• calculation of the position of the fixed point:

  To correctly position the polystyrene bread to be cut out compared to the fixed point, just refer to the diagram and following formulas:

  

  One has:

  xCe = b * Ce / (Ce-Cs)

  yCe = a * Ce / (Ce-Cs)

  xCs = xCe - b

  yCs = yCe - a

• an automatic machine :

  If the root and tips profiles are identical, it can be fine to cut out only one gauge and realize the wing while turning around the root gauge with the hot wire. It is necessary to find a solution to make the " fixed point "go up according to the twist. It is the object of this small assembly...

  Nothing simpler, one will use the displacement of the arc between the leading edge (BA) and trailing edge (BF) of the root gauge like instruction. This displacement is transmitted via a pulley and a string (pink on the diagram) to a rule articulated on the edge of the cutting table (the same one as the other machine...). By its own weight, the end of the rule will go down when the arc goes from BA to BF.

  As previously, the " fixed point " will be hang on a slide of drawer placed vertically to leave only one degree of freedom. (in blue on the diagram).

  The fixed point, there too, consists in a kneecap of 3 mm diameter.(brown on the diagram)

  The fixed point will be able to go up like a bucket out of a well using a cord rolled up around an axis and a pulley (red on the diagram). rather than the crank of the well, there is a wooden drum (tambour in french) on which is rolled up another string (green on the diagram). It is enough to pull on the string to make assemble the fixed point. And what will pull on this cord? It is the rule which goes down, of course (via another pulley)!

  We just need to compute at which place to fix this last pulley to obtain the wished twist, but this is really a piece of cake, with some multiplications... and up to us the twisted wings!

  

• the realization:

  No comments, it is enough to look at the pictures, there is even a film for those which want!

the overall picture gives an idea of the bazaar which reigns in my garage... You will note the presence of a screw clamp at the end of rule intended to compensate for the weight of the arc on the kneecap and thus tightening the wires. The system of pulleys fixed by double face on the cutting table are the same ones as for the other machine

• 

  The drums are made of a turned wood log, bored in its center then split to be able to be blocked on the axis by a screw at the level of semi-ray. For those which would not have a turning machine (or relations having one), one must be able to use rims of RC car...

  The axis is an end of steel log (8.1 mm in diameter) found in a do-it-yourself store, simply threaded on two angles bored to 8 mm then adjusted with the round file to turn without play.

The fixed point is a fall of aluminum angle screwed on the moving part of the drawer slide. A screw will be used as axis for the kneecap in prolongation of the cutting arc.

The film is downloadable here (1 Moctets):

 

This is the result for a 6° twisted wing. The tip profile is perfectly respected. The twist is very clearly seen

• calculation of the position of the intermediate pulley: :

  It is calculated starting from the following parameters:

  • - Xs = distance between the fixed point and the trailing edge at tip

    - Xe = distance between the fixed point and the trailing edge at root

    - d = diameter of the axis on which is rolled up the red wire

    - D = drum diameter

    - F = reeled pink string length when the arc goes the way BA BF. If the string is hung close to the

    root profile, F is not very different from the cord of root.

    - alpha = twist angle expressed in degrees

    - Cs = tip cord

    - Ce = root cord

    - N = distance between the articulation of the rule and the point of fastener of the pink string

    - n = what one seeks: outdistance between the articulation of the rule and the point of fastener of the

    green cord.

  For a twist of alpha degrees, the trailing edge of salmon must be raised of Cs*sin(alpha)

  Always according to Thalès, that implies that the fixed point must go up:

  Cs*sin(alpha)*Xe/(Xe-Xs)

   

  One can also dismount that Xe/(Xe-Xs) = Ce/(Ce-Cs)

  According to the report/ratio of the diameters betwee the axis and the drum, the green cord way is:

   

  F = (D/d)*Cs*sin(alpha)*Ce/(Ce-Cs)

   

  The intermediate pulley will thus be positioned with:

  n = N*f/F

   

  With the small angles of twist which one will carry out, one can replace the sine by the value of the angle

  in radians, that is to say, in fine:

  n = (N/F)*(D/d)*Cs*alpha*(3,1416 / 180)*Ce / (Ce-Cs)

   

  Lastly, if you have micro$oft EXCEL, you will find all the formulas ready to play with in the

  worksheet aile.xls.