Viewing Mt Helix from Cabrillo Point 16.2 miles
« on: September 16, 2018, 04:32:23 PM »
Post #1
Help me with my math.

363' observation point.
1372' target.
16.2 mile distance.

What's the elevation angle -- to the nearest tenth of a degree -- above level (eye level) for a flat earth and for a globe earth (r=3959 miles); no refraction?

I got:

+0.7° for flat earth.
+0.6° for a globe earth.

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Post #2

0.1° may be too small an increment to measure with confidence using Theodolite app.

Despite a no-refraction 175' "drop" difference between a flat and globe earth over 16.2 miles,  the angular delta may not be large enough to distinguish without more precise tools.

Could adding an 8-12x telephoto capability to the phone focal length help distinguish a vertical difference if 0.1°?

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Post #3

I think enough eyes have seen this, so I'm going to assume there are no corrections to the geometry.

Here are the geographic details:
Observation Point: Cabrillo National Monument
32.674005, -117.238946

Target Objective: Mount Helix Cross
32.767044, -116.983436

Last week, I noticed I could see the cross on Mt. Helix from a San Diego bay overlook near where I work. I can't take photographs from there, but I can go out to the Cabrillo Monument; and so I played with Google Earth and did the math to try to predict what the elevation above eye the cross should be from that observation point at the end of Point Loma.

I'd hoped to make predictions first before taking a sighting to avoid after-the-fact calculations, which can sometimes be skewed to match what is observed to what one wants to see.

I'm going to work with the Theodolite app to calibrate it and see if I can repeatedly, consistently take measurements to within 0.1°. I've tried this taking level sightings at the Coronado Islands 20 miles away, but the elevation data on the islands is much less certain than the ground elevation of Mt. Helix summit.

I'm also going to see if a telephoto multiplier lens for a smart phone will enhance the sighting at all.

Prediction going in is the Helix cross will be elevated +0.7° if earth is flat. +0.6° if earth is a globe.  Hoping I can do this in the mornings over the course of several days. I'll also thought it might be good to take some time lapse images for 15 minutes before and after each sighting to check for "Skunk Bay" -like dynamic atmospheric conditions.

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EDIT: Merged several posts to make OP adequate for upper fora. ~junker

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Post #4

Too much haze (smog) today for Theodolite/Phone camera, and I'm resigned to the fact that Theodolite app is just not up to the task. The cross hair line itself is 0.1° thick. And with needing to distinguish between 5.8° and 6.8°, getting level at 0.0° is critical. Even with repeated calibration, I felt the tool was inconsistent:


I was able to cut through the haze with my camera and, with a little color and clarity adjustment, was able to get a decent shot of Mt. Helix. (I'll link to the original image file since it's large.)

Could analyze angles and elevations using the Hilton Bayside tower in the foreground as a gauge. Has to be better than Theodolite, which just isn't cut out for what I set out to do here.

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Post #5

Cropped from original; resolution unchanged:



Can use this to figure vertical angle above level to Mt Helix summit (foot of the Helix cross). Need to find level first (different for FE and GE).

Photo taken from 363' elevation using a tripod set 4' high for a total of 367'
The Hilton, 26,739 feet away, is recorded as 385' tall on about 8' elevation (avg).


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Post #6

Calculating elevation angles above horizontal level for both Mt. Helix and Viejas Mountain, based on the measurements of the San Diego Hilton Bayfront tower:




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Post #7

Results recap:


The FE/GE "contest" starts to show more clearly with the unanticipated inclusion of Viejas. Helix measurements are too close to call and could easily be within margins of error.

I'll keep observing and measuring to see if different days/conditions produce different results; probably won't be able to bracket observations with time lapse imagery like I had hoped.

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Post #8

Tried again today...same spot...earlier in the day this time, but more haze/smog trapped in the basin than yesterday.

Widened the field of view to capture Cuyamaca Peak and add that to measurement. GE (with standard 7/6 refraction) consistently undershoots while FE calculation overshoot increases with range.

Having to take photo with heavy color processing to create contrast due to haze. Lots of blue. But otherwise, unaltered. Link to annotated photo in native 4000x2248 resolution is 2.2MB.
« Last Edit: September 20, 2018, 05:37:40 AM by Bobby Shafto »

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Re: Viewing Mt Helix from Cabrillo Point 16.2 miles
« Reply #1 on: September 21, 2018, 12:38:51 AM »
How did you establish the eyeline degree difference between GE and FE on the Hilton?

GE, Observer H=367', D=26739', H=385', bilsin's calc gives me 17.1' of drop, .0733 degrees of tilt

If I use a basic elevation calc, eyeline 18' below target at that distance, I get 0.0386 angle of elevation.

I have a feeling I'm using these calculations all wrong.

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Re: Viewing Mt Helix from Cabrillo Point 16.2 miles
« Reply #2 on: September 21, 2018, 12:47:14 AM »
Here are the specifics I got on the Hilton tower:


Re: Viewing Mt Helix from Cabrillo Point 16.2 miles
« Reply #3 on: September 21, 2018, 01:10:41 AM »
I took a slightly different path, but that's right (I think).

I have to go check my work, but I think I applied a 14' drop vice 17' (or 18'). That's the standard refraction calculation. I'm noticing that even standard refraction doesn't seem to be enough to make GE calculations match the measures from the images. Similar to the Turning Torso "challenge," FE geometry always anticipates a higher elevation angle whereas GE, even with standard refraction applied, is consistently lower than observed (albeit with less of a delta than FE).

But yeah, I figured a "drop" of the earth away from level, which is the difference between a flat and globe earth. I didn't use the angle to figure the pixel difference between FE and GE eye level, though that would have worked. I used the linear drop and then applied the ratio of pixel:feet to draw the level line for GE. Doing the trig just now, it looks like the angle is just slightly less than what you calculated, which makes sense if I used 14' for the drop and you used 18'.

Also, it's gnat's arse stuff, but your vertical distance of the Hilton didn't include the height above sea level. I've been using 8', so instead of 385' I've been using 393'.

Nice idea using Bislin's tool to model the difference between FE and GE calculations. Could add a 2nd distant target to visualize how the hill (Mt Helix) appears in the background relative to the hotel, and see how it compares.

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Also worth noting, I tried adding a 12x telephoto lens to my phone to see if it would help using the Theodolite app. It doesn't. It can help with precision of placing the cross hairs, but I think the lenses alter the optics, rendering the app unreliable for measuring elevation. (Might be a "collimation" issue Tom has mentioned in the past.)  I'll still keep experiment, but in the meantime, I think analysis of images using the Hilton as a gauge is the best approach without actual surveying tools.

« Last Edit: September 21, 2018, 06:09:54 AM by Bobby Shafto »

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Re: Viewing Mt Helix from Cabrillo Point 16.2 miles
« Reply #4 on: September 21, 2018, 09:35:47 PM »
Nice idea using Bislin's tool to model the difference between FE and GE calculations. Could add a 2nd distant target to visualize how the hill (Mt Helix) appears in the background relative to the hotel, and see how it compares.

I'm working on a pixel comparison now. But here's how Bilsins' calc lays out the Hilton to Mt Helix (no refraction):


Re: Viewing Mt Helix from Cabrillo Point 16.2 miles
« Reply #5 on: October 04, 2018, 09:16:56 PM »
I've been working leveling and calibrating my camera mount on my tripod to see if I can get it level for "eye-level" sighting. Back when I was trying to use the wire cube/water level apparatus, I didn't worry about getting the camera focal point level since the apparatus was supposed to provide that gauge. Instead, I just generally pointed the camera to best frame the picture.

But without some reference or trying to calculate what SHOULD be level from the image itself, I was wondering if there's enough precision with bubble levels to level the camera on the tripod so that "eye level" corresponds with the midpoint of the resulting shot. In other words, if shooting at 4000x2248, I'd want "eye level" to be at the horizontal pixel line at 1124 pixels vertically.

I've been able to get this to work across the width of 3 tennis courts, which I can be pretty certain provide a good level, flat surface where a 60" camera lens height corresponds to a 60" target 100' away, even at the longest focal length. But what is good enough for 100' may not be good enough for long ranges of a several miles.

I gave it a try today, shooting across San Diego Bay from the same Point Loma spot as where I'd taken the previous images in which I had tried to calculate where FE and GE 'eye level' lines might be.

Here's the result, unaltered other than reduced in size for inline posting.

The original is here (2.3MB)

By my measure, if I leveled the camera right, "eye-level" aligns with the top of the Bayfront Hilton.

This is about 12-13' higher than were I calculated it to be, and about 30' higher than it should be if the earth is flat.
13' over a distance of 26739' amounts to less than 3/1000th of a degree. 30' at that range is a little more than 0.06° vertical angle.

I figure the margin for error is a little less than 0.1° so this may not be a better way than simply doing the trigonometry based on known heights/distances and figuring out an angular gauge, but it provides a little confidence that the GE eye level is closer to truth than the FE eye level line. The more I do this, the more it confirms that objects appear declined in angle with distance. The "dip" is consistent, regardless of the method to detect it.