# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Refraction near the Horizon – Observation vs. Calculation**

**From:**Greg Rudzinski

**Date:**2013 Apr 5, 08:21 -0700

Brad and Bruce,

I sent a link for altitude refraction by mistake :( sorry. Try NGA which has several useful calculators to assist in the dip problem but the formulae used aren't listed.

http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_145&calcCode=03

Greg Rudzinski

Re: Refraction near the Horizon – Observation vs. Calculation

From: Brad Morris

Date: 2013 Apr 5, 11:05 -0400

Greg

That calculator includes altitude, temperature and pressure but surprisingly, not the height of eye.

Brad

On Apr 5, 2013 10:38 AM, "Greg Rudzinski" <gregrudzinski---com> wrote:

Bruce ,

Here is a link to a refraction calculator that includes corrections for temperature and pressure.

http://wise-obs.tau.ac.il/~eran/Wise/Util/Refraction.html

You might try measuring to a dip short point (.25 NM or so) up to the horizon as a check.

Greg Rudzinski

Re: Refraction near the Horizon – Observation vs. Calculation

From: Brad Morris

Date: 2013 Apr 5, 09:44 -0400

Hi Bruce

The equation models the effect of refraction by the air on a sphere the size of the earth. It uses standard pressure and temperature. If your pressure and/or temperature are non-standard, then the equation is not a good match. More advanced equations exist which include these parameters.

As to GPS units and vertical height. If the unit can average a position over time, then the height of the water and the height of the eye can be measured and the delta found. My Garmin averages at a 1 hertz rate. In order to get a reasonably error free value, I need about 1000 points. Alex noticed that the HoE was not good for short term or instantaneous reports. For large HoE, this won't matter, but for small HoE, its highly significant. Marcel's data, wherein the HoE is estimated --- Bill's results, if you recall, matched the standard equation when he measured the HoE, but meandered off when his HoE was from a mapped resource.

Let me emphasize this. The Height of Eye value is critically important for low HoE. The dip varies significantly for minor variation in height of eye when height of eye is low.

Brad

On Apr 5, 2013 9:15 AM, "Bruce J. Pennino" <bpennino.ce---net> wrote:

Thank you for posting this information. The text is just excellent and well written. My math/statistics background limits me , but I'll study the results.

I was interested to see that you use the equation for dip 1.76 sq rt H meters, which is the same as 0.971 sq rt H feet. I gather that this is the universally accepted equation, which I've proven to myself is from basic trig knowing the average radius of the earth? Right?

Bruce

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