# A DIY Theodolite for Measuring the Dip of the Horizon

#### Mick West

Staff member
You could just use an upside down glass mirror that you leveled. They you can put the camera a long distance behind it to get a narrow angle (which you can measure by the vertical amount of mirror in the image).

Although you really need a mirrored surface, as the glass complicates things.

#### Z.W. Wolf

##### Senior Member.
Yeah, you'd get two (at least) specular reflections with a normal mirror. You could use a sheet of reflective mylar glued onto an ordinary glass sheet.

Edit: Or maybe a one-way mirror with an opaque backing. I'm not sure how they make them these days. They used to have a deliberately thin layer of aluminum on one side, then another layer of glass to protect that layer.

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#### Clouds Givemethewillies

##### Senior Member
I'm not sure I get what this does. Can you explain a little?

I am new to this too! As I see it we are looking along a horizontal mirror. Assuming no distortion the direct image (lower) and the reflected image (upper) are symmetrical about the horizontal. Parts of the upper image are missing or poor and you can't quite see the horizon in the reflected image, however... you can see that the horizon in the direct image is below the axis of symmetry, particularly in the last image (Horizon Capture. png.)
Eyeballing through the cell I worked out that the smaller diameter semi-circle in the upper part is due to part of the lense being above the surface in this case.

#### Z.W. Wolf

##### Senior Member.
The line at the midway point between the horizon in the (complete) inverted image and the horizon in the normal image is the astronomical horizon (?)

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#### Clouds Givemethewillies

##### Senior Member
You could just use an upside down glass mirror that you leveled. They you can put the camera a long distance behind it to get a narrow angle (which you can measure by the vertical amount of mirror in the image).

Although you really need a mirrored surface, as the glass complicates things.

I can level my RCT tripod to 0.1 mrad., but then there is the problem of flat-earthers trusting me to do it right..

#### Clouds Givemethewillies

##### Senior Member
The line at the midway point between the horizon in the (complete) inverted image and the horizon in the normal image is the astronomical horizon (?)

It would be if you could see both clearly, but it is half way between any object in the image and its reflection, assuming no distortion.

#### Z.W. Wolf

##### Senior Member.
For what it's worth: the Vieux Port Pavilion in Marseille. Sadly for our purposes it is not level nor completely flat.

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#### Clouds Givemethewillies

##### Senior Member
I must do a time-lapse. The horizon seems to going up this evening..

#### Z.W. Wolf

##### Senior Member.
It would be if you could see both clearly, but it is half way between any object in the image and its reflection, assuming no distortion.

So the same should be true even if the plane of the film (sorry, sensor) is not perpendicular to the surface of the water. In that case you can use a physically larger lens angled up at the lower surface of the water.

#### Z.W. Wolf

##### Senior Member.
For anyone who is confused about the problem of focus: - how can you focus on the very close surface of the water and the distant horizon at the same time?

Focusing a camera on a mirror can be confusing at first. If a mirror is two feet from the camera you'd naturally think you have to focus the camera lens to two feet. And that is true if you want to focus on the frame around the mirror. But the image in the mirror is completely different. The focus range is still the distance of the light path. In other words an object 20 feet from the mirror is in focus when the lens is set to 20 feet. With one caveat. You also have to add the distance between the camera and the mirror surface. The upshot is the focus distance is the total length of the distance the light travels from object to camera.

This is focused on the surface of the mirror:

This one is focused on the image in the mirror:

So the camera in the Horizon Cam(tm) can be focused at infinity to see the both horizon and the image of the horizon on the surface of the water, even though the surface of the water is inches from the camera.

#### Clouds Givemethewillies

##### Senior Member
For anyone who is confused about the problem of focus: - how can you focus on the very close surface of the water and the distant horizon at the same time?

Focusing a camera on a mirror can be confusing at first. If a mirror is two feet from the camera you'd naturally think you have to focus the camera lens to two feet. And that is true if you want to focus on the frame around the mirror. But the image in the mirror is completely different. The focus range is still the distance of the light path. In other words an object 20 feet from the mirror is in focus when the lens is set to 20 feet. With one caveat. You also have to add the distance between the camera and the mirror surface. The upshot is the focus distance is the total length of the distance the light travels from object to camera.

This is focused on the surface of the mirror:

This one is focused on the image in the mirror:

So the camera in the Horizon Cam(tm) can be focused at infinity to see the both horizon and the image of the horizon on the surface of the water, even though the surface of the water is inches from the camera.

Exactly. I have made Horizon Cam Mega - 60cm. long. I was going to add a scale 1 metre away to read in milliradians, but then I thought about correcting for the water path, and put it on the back burner. I have bigger problems with bubbles! and the auto-exposure not working well looking down a long, black tube..

#### Z.W. Wolf

##### Senior Member.
The brightness and contrast of the inverted image is much better! So good that I can see very little difference from the normal image.

#### Clouds Givemethewillies

##### Senior Member
The brightness and contrast of the inverted image is much better! So good that I can see very little difference from the normal image.

On the down side you have to be more careful that the water is well mixed with the longer path length. I also get more consistent results with the cell indoors looking through a double-glazed upstairs window, and it is too big for that. Note that the two black 'arrows' do not show 'level', but the position of the water on the front window. They are actually two pieces of inclined black tape on the window and show the limit of what can be seen in the reflection. Pity I cannot use my S1 camera... For scale each white and green stripes are 2.5 metres with the lowest joint at 1.8 metres, giving a total height of 9.6 metres from the top of the jetty to the bottom of the light.

#### Clouds Givemethewillies

##### Senior Member
If only this filthy euro-air would go away I would take Horizon Cam Original up a hill!

Staff member
On a plane

#### Clouds Givemethewillies

##### Senior Member
You are lucky you did not get dragged off, screaming!

#### Mick West

Staff member
It was somewhat embarrassing.

#### deirdre

##### Senior Member.
It was somewhat embarrassing.
you're supposed to tell people it's for your kid's science experiment. That's what I do.

#### Mick West

Staff member
That was my plan, but they just ignored me.

##### Senior Member.
That was my plan, but they just ignored me.
Lol when you have a perfect excuse but nobody gives you a chance to use it... I know how that feels

#### Clouds Givemethewillies

##### Senior Member
Getting there slowly..

Edit: There is an error in the calculation. The dip should be multiplied by 2, which makes it consistent with the height of the 'lighthouse', but too large. Perhaps the water is too curved.. I have some isopropyl alcohol on order to try. The scaling is obtained by measuring the pixels between the top of the jetty and its reflection, and equating to _2_ x the dip of the jetty according to SHCC. (-1.5114 deg.)

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#### Clouds Givemethewillies

##### Senior Member
I found the problem with Horizon Cam. Bonus points for guessing what the problem is.

#### Mick West

Staff member
I found the problem with Horizon Cam. Bonus points for guessing what the problem is.

Refraction with the plastic and in/out air water interface?

#### Clouds Givemethewillies

##### Senior Member
Refraction with the plastic and in/out air water interface?

Yes, the front window needs to be accurately aligned vertically, which defeats the main purpose of being foolproof. I got it into my head that the effect cancels out, as do some other things, like a non-vertical back window, as the direct and reflected images move the same way there.

#### Mick West

Staff member
Someone on YouTube was complaining that my little torpedo level wasn't accurate enough to measure the dip. I agree it's just a cheap level not suitable for fine work. However I think it is sufficient for when on a plane. 30,000 feet gives a horizon dip of 3°. And even 2° is a surprisingly perceptible amount.
My new level on the bottom (which I actually needed for some stairs I'm building) is much more accurate. It also has an adjustable angle level, which I set to 2°. This then required a 0.25" rise at the other end. The pivoting section is 7" long. Verifying the angle: asin(0.25/7) in degrees = 2.05°, and 3° is about 3/8"

So my crappy little level with a pen on top is accurate enough to detect a 3° dip (providing you can see some kind of horizon).

#### Clouds Givemethewillies

##### Senior Member
Someone on YouTube was complaining that my little torpedo level wasn't accurate enough to measure the dip. I agree it's just a cheap level not suitable for fine work. However I think it is sufficient for when on a plane. 30,000 feet gives a horizon dip of 3°. And even 2° is a surprisingly perceptible amount.
My new level on the bottom (which I actually needed for some stairs I'm building) is much more accurate. It also has an adjustable angle level, which I set to 2°. This then required a 0.25" rise at the other end. The pivoting section is 7" long. Verifying the angle: asin(0.25/7) in degrees = 2.05°, and 3° is about 3/8"

So my crappy little level with a pen on top is accurate enough to detect a 3° dip (providing you can see some kind of horizon).

I used a "Replacement-Level-Glass-Vial-Spirit-Bubble-Level-Accurate-Colours-70mm-35mm" that I found on Ebay. - 20 seconds/division. I had to make a mount for it. It is too sensitive to use without a very stable platform. I also got a second hand "Brass-amp-Glass-Quality-Circular-Bubble-Level-Bulls-eye-Surveying-Equipment" Both can be seen in the picture of mirror horizon cam.

If you want to actually measure angles, you can get digital levels, but they need to be set up properly first.

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#### Mick West

Staff member
If you want to actually measure angles, you can get digital levels, but they need to be set up properly first.

I was temped by one at Home Depot, but figured digital just leaves you open to cries of fake. Figured I could use the adjustable level, but really it's difficult to read even 1° from it. Calculating the angle from the linear displacement of the end is very accurate though. 0.6 degrees per inch in the setup I have in the OP (48" behind a 48" level), so I'd say accurate to around 0.05°. Maybe you could try that method where you are?

#### Clouds Givemethewillies

##### Senior Member
I was temped by one at Home Depot, but figured digital just leaves you open to cries of fake. Figured I could use the adjustable level, but really it's difficult to read even 1° from it. Calculating the angle from the linear displacement of the end is very accurate though. 0.6 degrees per inch in the setup I have in the OP (48" behind a 48" level), so I'd say accurate to around 0.05°. Maybe you could try that method where you are?
Will do. I was wondering if I could get a decent focus on both the level and horizon. I just got a long focal length lense for my webcam, it might be my best bet. Big improvement in resolution over the PI cam but the lense is probably too big for mirror cam. See attached:

#### Clouds Givemethewillies

##### Senior Member
Should work on a better day and a bit of practice. For scale the flanges are 125mm. square and 600mm. apart. F11 Fuji S1 camera.
Levelling is quite critical. .

#### Clouds Givemethewillies

##### Senior Member
I was temped by one at Home Depot, but figured digital just leaves you open to cries of fake. Figured I could use the adjustable level, but really it's difficult to read even 1° from it. Calculating the angle from the linear displacement of the end is very accurate though. 0.6 degrees per inch in the setup I have in the OP (48" behind a 48" level), so I'd say accurate to around 0.05°. Maybe you could try that method where you are?

Got it! I used an aluminium ladder. The front sight is 294cm. away from the ruler

.

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#### Clouds Givemethewillies

##### Senior Member
This probably belongs somewhere else, but I think near-IR has its uses in reducing the effect of haze. Two photos, one with IR blocking, and one with visible blocking/IR pass filters - webcam.

#### Mick West

Staff member
Got it! I used an aluminium ladder. The front sight is 294cm. away from the ruler

.

I'm a little confused by your setup there. Which level edge are you measuring from?

#### Clouds Givemethewillies

##### Senior Member
I am looking along the length of the ladder. there are two bars across the ladder resting on it. The front one is a bit of aluminium angle, and the back one is a bit of aluminium strip with the bottom edge aligned with a centimetre mark on the bit of plastic ruler. So you look where the bottom edge of the (front) angle (which I tried to align with the horizon) is on the ruler. I make it 11mm. 11/2940*360/(2*Pi) = 0.214 degrees. On the low side of recent measurements.

ps. The ladder looked pretty straight sighting along it. Also it is supported in the middle where the level is, so any sag should tend to balance out.

I could do with a flat section ruler, the bevelled edges spoil things a bit.

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#### Mick West

Staff member
the back one is a bit of aluminium strip with the bottom edge aligned with a centimetre mark on the bit of plastic ruler.

I'm still confused. You seem to be saying this is level:

And yet it's pointing below the horizon.

#### Mick West

Staff member
Oh wait, I think I get it now. Level is from the back strip to the bottom of the angle strip, so it's the other way around to how I did it. You are measuring from the back, I was measuring from the front.

#### Clouds Givemethewillies

##### Senior Member
Oh wait, I think I get it now. Level is from the back strip to the bottom of the angle strip, so it's the other way around to how I did it. You are measuring from the back, I was measuring from the front.

The front was hanging over a glasshouse, so I risked my life getting the angle into position!

#### Clouds Givemethewillies

##### Senior Member
The mirror horizon cam is about 3 metres higher so should actually give a larger magnitude, as it happens.. I think the ladder is about 51 metres above sea level, but it is difficult to tell, being on a slope, and I have not really looked in to sea level v GPS datum.

#### Trailblazer

##### Moderator
Staff member
I think the ladder is about 51 metres above sea level, but it is difficult to tell, being on a slope, and I have not really looked in to sea level v GPS datum.
You should be able to check that to a reasonable degree of accuracy by going to a local spot height as marked on the Ordnance Survey map and comparing what your GPS says, taking a few readings to average it.

This is a useful link for looking at the large-scale maps http://www.geograph.org.uk/showmap.php?gridref=SN580810

Or this shows heights to 0.1 metres in your area: http://map.ceredigion.gov.uk/connect/?mapcfg=PLANNING_APPLICATIONS

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