If an aircraft flies over my QTH at say, 35,000 ft, how far will it remain "in line of sight" i.e before it dips below the horizon?

I am trying to work out how far I can expect to keep receiving S band signals on the plane plotter program.

73

Wayne VK4WDM

## Is there a calculation for this?

### Re: Is there a calculation for this?

UKW tools or maybe Radio Mobile. UKW allows you to input the height of the antenna and it calcualtes propogation for varying power and frequency etc.

Compton

VK2HRX

Compton

VK2HRX

Compton

VK2HRX

QF56ne, Ryde, Sydney

VK2HRX

QF56ne, Ryde, Sydney

### Re: Is there a calculation for this?

Hi Wayne,

The distance you will be able to 'see' to the horizon is approximately 3.856 x Sqrt(h) where h is your observation (or antenna) height above sea level (or surrounding flat ground) in m, and the distance calculated is in km.

The distance the plane pilot will be able to 'see' works to the same formula too, but their answer is of course going to be much larger.

eg. You (or your antenna) are at 2m. Your horizon is calculated as 5.45km.

Plane is at 10,000m. Their horizon is calculated as 385.6km.

Now the crunch, and maybe someone can help... There is a factor between these two different horizons that will determine how far out you can see the plane. It's not straight division since that would mean as you elevate your position the distance would get smaller, not bigger.

Also, for timing, you then need to know his (or her, these days!) speed in km/hr, and then you can work out how quickly it will cover the calculated horizon distance; distance in km divided by speed in km/hr to get an answer in decimal parts of an hour.

That only applies though for a timing you start for a plane that flies directly over your theoretical zenith (the line vertically upwards from your QTH). The chances of this are staggeringly small, so it will all be approximations.

Also check this page out for more formulas that may or may not help: http://en.wikipedia.org/wiki/File:HorizonDistance.png

73 - Rob VK2GOM / G0MOH

The distance you will be able to 'see' to the horizon is approximately 3.856 x Sqrt(h) where h is your observation (or antenna) height above sea level (or surrounding flat ground) in m, and the distance calculated is in km.

The distance the plane pilot will be able to 'see' works to the same formula too, but their answer is of course going to be much larger.

eg. You (or your antenna) are at 2m. Your horizon is calculated as 5.45km.

Plane is at 10,000m. Their horizon is calculated as 385.6km.

Now the crunch, and maybe someone can help... There is a factor between these two different horizons that will determine how far out you can see the plane. It's not straight division since that would mean as you elevate your position the distance would get smaller, not bigger.

**EDIT:**I think it may even be as simple as Sqrt(Your horizon x plane horizon)*Can anyone verify this?*Also, for timing, you then need to know his (or her, these days!) speed in km/hr, and then you can work out how quickly it will cover the calculated horizon distance; distance in km divided by speed in km/hr to get an answer in decimal parts of an hour.

That only applies though for a timing you start for a plane that flies directly over your theoretical zenith (the line vertically upwards from your QTH). The chances of this are staggeringly small, so it will all be approximations.

Also check this page out for more formulas that may or may not help: http://en.wikipedia.org/wiki/File:HorizonDistance.png

73 - Rob VK2GOM / G0MOH

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### Re: Is there a calculation for this?

Isn't the maximum range just the sum of the horizon distances? i.e. 385.6 + 5.45 = 391 kmVK2GOM wrote:Your horizon is calculated as 5.45km ... Their horizon is calculated as 385.6km.

However, for a radio path, you also need to account for the bending of the RF path - often referred to as the 4/3rds rule.

So, the radio horizon is more like 4.12 x sqrt(h) or about 417 km for this example.

Regards,

Dave.