Well for one, I wasn’t considering incandescent. Two, if the relflector is shallow enough, a hemispheric surface is very close to a paraboloid surface, so it’s probably partially a matter of manufacturing expedience; I highly doubt Mr. Mag used raytracing software to design his reflector. Third, I can’t say I’m particularly fond of the beam pattern of those Mags, though when I was younger that was the high end. Fourth, it seems their LED offerings have parabolic rather than spherical reflectors.
There’s absolutely no such thing as the perfect beam - only the best beam for the particular use. The shape will determine the amount of spill versus throw. The focal point is determined by the equation for the parabola. The reason a particular LED needs specific focusing is because different LEDs have different LES heights off the surface of the PCB. Even then manufactureing doesn’t give a 100% perfect focal plane and spacers or grinding may be necessary for a perfect focus.
No they don’t. They use paraboloid reflectors just like led flashlights. The only difference is that in a led light the bottom of the parabole is cut off because leds do not put out light backwards.
It is just one formula, that of a parabole. In that formula you can vary the focal length for a deeper or shallower parabole, and you can choose where to position the cut-off depending on what width/length ratio of the reflector you want. But those are all still paraboles. Anything diverging from a parabolic shape of a reflector will reduce throw and will generally create a less pretty beam.
Sorry Jos, that is not correct. The Incan Mag has a bowl shape reflector that is quite different from the newer LED lights reflector. I have multiples here as well as literally all the internal components… many times over. I also have all of Old Lumens kit from when he worked the Maglites.
In fact, ALL parabola are equivalent to one another in shape, just scaled up or down. Take a big reflector like a BLF GT. If you extended the parabolic surface out further, then walked back, it would be proportionately equivalent to a small reflector that is narrow and deep. In other words, given a point source of light, a large parabolic reflector and small one with a half-angle opening of 30 degrees should reflect and spill the same amount of light, given a reflector that is 100% efficient. Since that’s not the case, it would seem clear that the larger reflector would collect light more efficiently since it has the larger surface area. But we know all this intuitively - we get more throw out of a light by fitting LEDs with smaller LESs onto larger reflectors. We also know that can be a bear to dial in the focus, and that defects in the reflector are more readily seen with smaller LES. We also find that certain reflector and LED combinations don’t work too well to our eyes and preferences.
The actual parabolic equation is y = ax^2 + bx + c, where a determines how fast x grows in relation to y, b is the displacement from center along the x axis, and c along the y. When I was in high school many moons ago, I was probably the best computer science student in my class, which didn’t say much LOL. But I actually ended up teaching the second half of the school year, and one the projects I did with the class was make an isometric drawing of a paraboloid on the computer screen, and how to convert a 3D image to isometric (and eventually perspective.) And we did this all on BASIC, with a 320 x 240 resolution monochrome CRT monitor. I have the papers still somewhere, as the math eludes me a little bit on how a 3D-2D transformation is accomplished, but it’s all actually relatively simple trigonometry. Little did I know then that some of this stuff was actually useful when I built my first CNC machine and couldn’t afford a good CAM system.
no, there’s no hemispherial or hyperbolical shaped reflectors in Maglites or other incandescent flashlights, they will not give you a proper hotspot.
Example: the MiniMag, found a patent drawing that clearly shows a parabolical reflector:
But man, that is a hyperbola not a parabola, the dimensions dictate… Ok, so not hemispherical like a round bowl, but not the elongated parabolic formula that works for LED’s either, not by a long shot. The reason is the side emitting incandescent has different requirements. A hyperbola is a form of parabola in that it is a curved line, so it’s difficult to argue the science. Apples are not steak, steak isn’t a vegetable. Mag incan’s reflectors don’t work with LED’s.
Whatever the science, the differences are night and day and one won’t work with the other’s output source. In the sense that any curved line is a parabola then that is correct. But in the sense that a Hyperbola is on a different formula then the difference is very real. There are plenty of other flashlights that do use a hemispherical shaped reflector. They existed for a hundred years. So maybe my Maglite example was slightly off, still an example of a bad curve for LED’s.
I talk too much, we all know that. I don’t mean it to be an argument just a discussion. Build a light with an LED using an incandescent Maglite reflector and show me the beam profile, I’ll shut up. I already know the answer because I’ve already done the builds…
I think some of those pirate searchlights from the days when they illuminated them with a candle may have just had a spherical reflector… at least the poor pirates!
It would be relatively easy to test if the reflector is indeed hyperbolic or parabolic. Build a rig where you can set the axis of the reflector parallel to a flat surface. Make a cardboard cutout of the shape of the center of the reflector and place it in there. Then take a laser pointer, set its beam parallel to the reflector’s axis, and shine it at different spots on the reflector. If it’s parabolic it would hit the same spot on the cardboard. But dimensions alone cannot truly dictate the shape, because the difference can be so subtle that without knowing what (if any) equation was used to generate the surface. A hyperbola is a special case of a conic section, where you have a cone mirrored, and a plane intersecting both cones. So a hyperbolic equation has 2 solutions. A parabola is formed when the intersecting plane touches only 1 cone. Thus a parabolic equation has only 1 solution. So the difference between a hyperbola and a parabola can be in the order of fractions of fractions of a degree. Impossible to tell by eye. Also, if the surface of a paraboloid was continued indefinitely it would approach but never reach parallel with the axis of the cone. A hyperbola extended into infinity would approach but never reach the half-angle of the cone.
But could an incan Mag reflector be shaped differently? Absolutely. But unless they make an incan BLF GT this argument is irrelevant. I think the next great mod should be a BLF GT Xenon. THAT would be cool…
Not necessarily. The requirement for a parabola is that the plane only intersects one cone, and the intersection of plane and cone does not form a closed curve, such as an ellipse or circle. The hyperbola’s requirement is that the plane must intersect both cones, regardless of the angle of the plane. If you graph a double cone on Cartesian coordiantes, where the axis is on the Z and the points are on 0,0,0 then the formula is Z = ax^2 + by^2 where a and b determine the spread in x and y. A regular cone is a special case where a and b are equal, thus determining the spread of the cone equally. So if you solve for all points on the Z axis you get a positive and negative cone.
Another way to think about this - hyperbolae are formed when the intersecting plane, relative to the axis, has an angle greater than 0 and less than the half angle of the cone. A parabola is formed when the angle of the plane, relative to the axis, is greater than the half angle - thus, it is impossible for it to intersect both cones.
So, the very definitions vary as much as the opinions?
Given that the slice is parallel to the angle then it cannot touch the second cone. Also, given that a hyperbola is in parallel with the axis then it will have no choice but to intersect both cones.
pa·rab·o·la
/pəˈrabələ/Submit
noun
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
conic section parabola
We also get a parabola when we slice through a cone (the slice must be parallel to the side of the cone).
So the parabola is a conic section (a section of a cone).
And another… A parabola is the curve formed by the intersection of a plane and a cone, when the plane is at the same slant as the side of the cone.
I’ve studied this for years as I’ve been building lights and shaping reflectors for them ever since Old Lumens first scratch build. I have nothing better to do so I can discuss this til the end of time…
If the plane is at the half-angle of the two cones passing through the apex the resulting intersection is a straight line. If the plane passes through the axis of the cones the resulting intersection is two straight lines.
But yes those definitions are right for parabola. I meant ellipse when the angle is greater than that of the side but was typing too fast. The plane defining a hyperbola however need not be parallel to the axis, as long as the angle is greater than 0 and less than the half-angle of the cone. That should be obvious as the plane is infinite in size.
Also the path of a projectile only follows a parabolic path if there are no other forces acting upon it - i.e. air resistance - and it’s speed remained constant. So the rate of descent would not equal the rate of ascent unless the projectile were in a vacuum.
But it should be pretty clear by your own definitions that every parabola is geometrically proportional. So there’s no real “design” as far as shape or equation; it’s making them the right size with the right opening for the emitter used and its intended purpose.
The point is, there is a very fine line between parabola and hyperbola, and both can look exactly the same to the naked eye.
Indeed, a tremendous amount of research has been spent determining the exacting formula for long range throw. I know this well as I have been on the developing teams determining this information. It really is exacting, the GT missed by a little, the MF03 missed, the TN42 is maybe closest but somewhat too small, absolute throw distance from a reflector is a refined art and one that has not been developed to it’s fullest potential at this point.
The 4 reflector cups of the GT4 show good promise and I really do look forward to seeing them in action. I do like the compromise to use 70.2’s for more output with larger spot in order to make a more effective search light that helps the unaided eye find the subject in question. I have potential here to use lights that are capable of putting light on target at 2 miles, but of course my eyes cannot determine what I’m seeing at that range in any real detail only that I am seeing light on target. For me, more light on a closer target is most welcome. IE: is that a striped skunk or a spotted skunk? 2 stripes or 3? Some varieties are more aggressive than others and given identification proper action is more easily determined… I value the information as to whether to avoid altogether, continue on with some risk, or forget about it and go on about my business.
To sum up: Having an exact parabola is only needed if one has a very close approximation to the ideal point source. The small filaments in the original Surefire P60s and P90s were about as close as one could get. An equivalent option would be some of the HID bulbs with a very small arc length, but there the electrode presence disrupts the symmetry of the beam.
So if you aren’t going to have a perfect point source, you are pretty much free to modify the basic parabola to accomplish whatever your design goals are. A goal of a small diameter very bright center beam (hot spot) will result in a different shape than the goal of more spill and/or a more even beam. That is one of the reasons some designers use aspheric lenses instead of reflectors to shape their beam. [Please don’t let this start a discussion on lenses vs reflectors]
I still find it easiest to visualize a perfect parabola when talking about reflectors and beam patterns and throw distances. At one time in my sordid past I spent six months developing software to design and manipulate parabolas for a CAD/CAM package (anyone remember Applicon?).
