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[技术] 简单的抛物线太阳能制作

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发表于 2010-9-4 13:52:01 | 显示全部楼层 |阅读模式
一组抛物线组成了一个抛物面,这是一个很简单的道理,我们就是用这个简单的抛物线组成了一个抛物面来制作一个太阳能的。是不是很简单呀。下面的过程就是抛物面太阳能,看了图片相信你一定会认为我的观点的——简单。

Parabolic mirror surfaces are found wherever energy needs to be focused efficiently and accurately. You find them built into car headlights, spotlights as well as astronomical telescopes. Here we explore the parabola to design solar heaters.



这两个抛物面太阳能是不是超简单呀?
Photo 1. Two photos of a small solar heater made from plastic mirror sheet bent into a parabola shape by a wooden template. There is a black temperature data logger at the focus which is where the solar energy is being concentrated. Apart from the screws and plastic mirror all the parabola 'bits' were made from scrap. The shape of the parabola is given by equation [1], see table 1.
The Parabola
When Sun light (parallel rays) falls onto a correctly aligned parabolic mirror it will be reflected back towards a single point known as the focus. The parabolic mirror therefore directs the energy arriving over its surface to a 'hot spot' at the focus. You can use this energy to heat something.
The basic shape of a parabola is derived from the equation:
y² = 4ax [1]
Where y represents the distance away from the mirror centre and x represents the 'height above' the centre, see figure 1 and 2. The c**tant a is known as the focal length - the distance from the origin to the focus point.


制作原理图就不用我多说了吧。

Figure 1. The basic geometry of a parabola mirror. Light rays coming from infinity will tend to be reflected towards a point called the focus.
If we want to make a parabolic reflector to our own particular specification i.e. in terms of its size D (i.e. having maximum y = D/2), height h and focal length a, then equation 1 becomes:
a = D²/16h [2]
 楼主| 发表于 2010-9-4 13:52:19 | 显示全部楼层
本帖最后由 fengxue 于 2010-9-4 13:55 编辑

A simple curved plane (rather than dish shape) solar heater is shown in photo 1 and we shall use this as an example, of course what follows can also be used for a full 'dish shaped' parabola and for much larger designs.


这里计算抛物面太阳能焦点。

Figure 2. Parabolic surface made using i) a cut-out template or ii) by thin sheet fixed to vertical wooden supports. The position (y*) and height (x*) of each support (point) is calculated from the equation 1 and 3. A set of x and y values for the model in photo 1 is give in table 1. D-length, h-height, a-focus and j (an offset used to make the template version, see text).
To make it easy to locate the focal point when we are using it, I chose to design the mirror surface height (h) to be the same value as a - the focus distance above the canter of the mirror (so a = h in this example 11 cm). In this case finding the focus is simple - imagine a line going across the top of the device, the centre of this line is where the focus is.
Rearranging equation 2 we get the diameter / length of the solar heater D to be:
D² = 16ah, so using h = a = 11 cm we get:
D = √(16x11x11) = √(1936) = 44 cm
We have y² = 4ax and a = 11 cm
For the solar heater shown in photo 1 we get x = y²/44
[3] (all dimensi** in cm)
Now that we have chosen the basic quantities for the parabola we can compute the x and y coordinates from equation 1 and 3. Some of these are tabulated in table 1. To re-cap, the y axis represents the distance away from the mirrors centre while x represents the 'height' above the base, the lowest point of the mirror (its centre).
You can also make a parabola support by cutting two side (parabola shaped) templates, see photo 1. In this case when marking up simply add a few cm (j in figure 2) to all the x values otherwise the template will diminish to zero thickness at the centre and it will all fall apart!
Table 1 - y and x values derived from equation 3 for the parabolic solar heater shown in photo 1.
 楼主| 发表于 2010-9-4 13:56:22 | 显示全部楼层
±y (cm)                                                                                                y²                                                                                                y²/44                                                                                                x (cm)                                       
                                                        0                                                                0                                        0                                        0                               
                        1                                        1                1/44                0               
2                                        4                4/44                0.1               
                        3                                        9                9/44                0.2               
                4                                16                16/44                0.3               
                        5                        25                25/44                0.6               
                        6                                        36                36/44                0.8               
                7                42                42/44                0.9               
                        8                                        64                        64/44                1.5                       
                        ...                                        ...                ...                ...               
                        20                400                400/44                9.1               

and so on for larger values of y




Rough Science solar heater
In the second BBC TV Rough Science series Ellen McCallie and I made a large solar heater. A piece of straight wooden plank was cut for the base (D=2m). The central half way point was marked. At ±y cm distances every 15 cm or so, from the centre, vertical battens were attached having heights of x cm. When these were all in place a thin piece of plywood was put over the top to complete the parabolic surface. Our mirror had a surface area of about 1m2.
 楼主| 发表于 2010-9-4 13:56:39 | 显示全部楼层
Mirrors
Various mirror surfaces can be used to cover the parabola surface. The Rough Science device used fragments of broken mirror cemented to the parabolic surface (see Note 1 below). I have also used small 3 cm mirror squares from an arts supplier as well as aluminium kitchen foil (see note 4). Flexible mirrored plastic sheet is also available which has excellent properties, it can also be cut with scissors and is very safe, easy to manipulate and change.
Locating the Sun and setting up the device
Obviously there needs to be direct sunlight to get any decent heating from the reflector but it is also important that the device is correctly aligned to the Sun. If the base can be extended a little and a bolt fixed through so that it points out at right angles then the bolts shadow should disappear when the device is pointing directly at the Sun. Obviously you can also adjust the hot spot for maximum brightness by trial and error.
What to heat?
At the equator there is about 1kW of solar power for every square meter of collecting surface. The small heater shown in photo 1 only has an area of about 1/20th m² but it still makes a good dem**tration. Larger parabolic system having say 1-2 m² surface area should have enough energy to boil water in a small kettle for a cup of tea! The amount of heating obviously depends on the time of year / day, the weather and 'strength' of the sun (your latitude). Painting the kettle mat black with fire proof paint helps. Putting a large transparent plastic bag around the kettle also helps reduce heat loss (it acts like a mini green house). It would be fun to try cooking an egg on a flat plate arranged at the focus.


Satellite dish - a section of a much larger parabolic surface
The satellite dish
Energy falling on to a correctly aligned parabolic mirror (of collecting surface area A) will be reflected to the focal point. However if you heat something large at this focus it will block the light getting to the mirror, effectively reducing A. There is a way of getting around this problem however.
Imagine a giant parabolic dish most of which we cut away to leave behind just a parabolic section of area A, near to the circumference. This remaining section will collect the same amount of energy as an ideal (full) parabola of the same area. Any energy falling on to this section would still be reflected to the focus point although now this point seems rather off-set from the dish. This is a useful modification as equipment put at the focal point will now not block the arriving energy. This technique is often used in satellite TV receiving dishes where the TV receiver head (a small electronic device) is placed at the focus (which now seems off-set) so the equipment does not block the path of the weak TV signals coming in from the space satellites (see above).
发表于 2011-1-27 10:38:41 | 显示全部楼层
hehe, so ich werde denn posten
发表于 2011-1-30 12:27:13 | 显示全部楼层
很棒的小太阳能灶
发表于 2011-2-3 15:13:59 | 显示全部楼层
英文翻译过来理解有点费解。 东西不错
发表于 2011-8-8 00:21:55 | 显示全部楼层
光接收面太少了,一般一平方米功率在700w左右。
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