Hi, first time poster here.
I'm a mechanical engineering student and I would like to know a couple of things about the surface of a paraboloid shape.
First I'd like to tell you more about what I'm trying to do with and why I need to know more about paraboloids.
I help run a medium sized hobby workshop intended for students. We have quite a large set of metal and woodworking tool at our disposal. For some future projects I have in mind (a certain type of antenna and a jet nozzle) it would be very nice if i could manufacture a paraboloid out of sheet metal. As you can imagine this is not an easy task. A professional workshop would have specialized tool and a press specifically designed for shaping sheet metal, but obviously we don't have such a tool since they cost a fortune and are only worth getting for professional use.
We do have a sheet metal cutter for circular shapes though, and I know that the flattened surface of a cone (with its tip missing) looks something like an arc. So it would be really easy to make a cone from sheet metal by cutting a circle, and then cutting another circle out of the original one to get a ring type shape, and finally cut a segment out of that.
Now to my question to you smart people of this forum: Is it possible to to do a similar thing to a paraboloid surface where you have a flat peace of material of a certain shape and by rolling it in a certain way you get the wanted shape? What would the flat surface shape look like? And is that even mathematically possible to do so without stretching the sheet metal into shape.
I did put some thought into it myself, and the only way I could think of solving the problem was by following the same steps as with the cone shape but before rolling the arc into a cone to hammer the 2D sheet metal arc into a 3D curved arc with some depth to it as shown in the picture.
View attachment 9626
Thank you for your responses!
I'm a mechanical engineering student and I would like to know a couple of things about the surface of a paraboloid shape.
First I'd like to tell you more about what I'm trying to do with and why I need to know more about paraboloids.
I help run a medium sized hobby workshop intended for students. We have quite a large set of metal and woodworking tool at our disposal. For some future projects I have in mind (a certain type of antenna and a jet nozzle) it would be very nice if i could manufacture a paraboloid out of sheet metal. As you can imagine this is not an easy task. A professional workshop would have specialized tool and a press specifically designed for shaping sheet metal, but obviously we don't have such a tool since they cost a fortune and are only worth getting for professional use.
We do have a sheet metal cutter for circular shapes though, and I know that the flattened surface of a cone (with its tip missing) looks something like an arc. So it would be really easy to make a cone from sheet metal by cutting a circle, and then cutting another circle out of the original one to get a ring type shape, and finally cut a segment out of that.
Now to my question to you smart people of this forum: Is it possible to to do a similar thing to a paraboloid surface where you have a flat peace of material of a certain shape and by rolling it in a certain way you get the wanted shape? What would the flat surface shape look like? And is that even mathematically possible to do so without stretching the sheet metal into shape.
I did put some thought into it myself, and the only way I could think of solving the problem was by following the same steps as with the cone shape but before rolling the arc into a cone to hammer the 2D sheet metal arc into a 3D curved arc with some depth to it as shown in the picture.
View attachment 9626
Thank you for your responses!