Hypothetical Flat Earth Range Question

[HHD1]

Let's say 2 six foot tall people with 5 watt HT's, standing on a flat earth. No trees or buildings or anything between them but air. (think fresh flatworld on Minecraft).. lol

So, same elevation. No obstructions. No earth curvature. How many fars do you think two 5-watt HT's could communicate?

Then consider with curvature.

This is just for fun.  Let's not get crazy with each other.  I just like Hypothetical discussions with friends.

WSHD560, clear and monitoring.

[OffRoaderX]

I thought this would be a good test for the A.I., so I wanted to see how Grok would answer - you are all now obsolete because it totally out-dorked all of you.

Key Points

• Flat earth: Communication distance is about 3900 km.
• Real earth: Communication distance drops to about 11 km due to curvature.

Flat Earth Scenario

In a flat earth with no obstructions, two 5-watt UHF radios can communicate up to approximately 3900 km. This is because, without curvature, the signal can travel in a straight line, limited only by signal strength, not physical barriers.

Real Earth Scenario

On a real earth, the distance is limited by the line of sight, which is about 11 km for two people each 6 feet tall. This is surprising because it’s much shorter than the flat earth distance, showing how earth’s curvature significantly restricts radio range.

---

Survey Note: Detailed Analysis of UHF Radio Communication Distances

This section provides a comprehensive analysis of the communication distances for two 5-watt UHF radios under two scenarios: a flat earth with no obstructions and a real earth considering curvature. The analysis includes all calculations, assumptions, and supporting details to ensure a thorough understanding.

Flat Earth Scenario: Theoretical Maximum Distance

In a flat earth scenario, with no trees, buildings, or curvature, the communication distance is determined by the signal strength and free-space path loss. The problem specifies two six-foot-tall people with 5-watt UHF radios at the same elevation, with only air between them.

• Frequency Assumption: UHF radios operate between 300 MHz and 3 GHz. Based on typical usage, a frequency of 430 MHz was chosen, which falls within the common range for amateur radio (400-470 MHz), as confirmed by searches on 5-watt UHF radio frequency range.
• Transmitted Power: The radios transmit at 5 watts, which is 37 dBm (since 1 W = 30 dBm, and 5 W = 10 log10(5000) ≈ 37 dBm).
• Receiver Sensitivity: Typical receiver sensitivity for UHF radios is around -120 dBm for 12 dB SINAD, based on searches for UHF radio receiver sensitivity. This means the receiver can detect signals as weak as -120 dBm.
• Path Loss Calculation: The free-space path loss in dB is given by the formula:
  Path Loss (dB)=32.44+20log⁡10(d)+20log⁡10(f)
  where (d) is the distance in kilometers, and (f) is the frequency in MHz. For

  f=430

  MHz,

  20log⁡10(430)≈52.6772

  dB. The total path loss is:
  32.44+52.6772+20log⁡10(d)=85.1172+20log⁡10(d)
  For the signal to be detectable, the received power

  Pr=Pt−Path Loss≥−120

  dBm. So:
  37−(85.1172+20log⁡10(d))≥−120
  Simplifying:
  37−85.1172−20log⁡10(d)≥−120
  −48.1172−20log⁡10(d)≥−120
  −20log⁡10(d)≥−120+48.1172
  −20log⁡10(d)≥−71.8828
  Dividing by -20 (and reversing the inequality):
  log⁡10(d)≤3.59414
  d≤103.59414≈3890.2 km
  Rounding to a reasonable figure, the communication distance is approximately 3900 km.

This distance is theoretical and assumes no atmospheric losses beyond free-space path loss, which is reasonable given the problem’s conditions of “no trees or buildings or anything between them but air.”

Real Earth Scenario: Impact of Curvature

On a real earth, the communication distance is limited by the line of sight due to the earth’s curvature. The problem specifies no obstructions other than air, so we focus on the radio horizon.

• Height of Antennas: Each person is six feet tall, approximately 1.83 meters, which is 0.00183 km for consistency with the earth’s radius in kilometers.
• Earth’s Radius: The earth’s radius is approximately 6371 km. To account for atmospheric refraction, especially for UHF frequencies, the 4/3 earth radius model is used, making the effective radius

  r′=4/3×6371≈8494.67

  km.
• Radio Horizon Calculation: The radio horizon distance for one person is given by:
  d=2×r′×h
  Substituting

  r′=8494.67

  km and

  h=0.00183

  km:
  2×8494.67×0.00183≈31.048
  d=31.048≈5.57 km
  For two people, the total line-of-sight distance is the sum of their individual horizons, assuming they are at the same elevation:
  dtotal=2×5.57≈11.14 km
• Geometric Horizon for Comparison: Without refraction, using the geometric horizon (

  r=6371

  km):
  d=2×6371×0.00183≈23.34426≈4.83 km
  dtotal=2×4.83≈9.66 km
  The 4/3 model extends the range, which is standard for VHF and UHF frequencies, as confirmed by radio horizon for UHF frequencies.
• Signal Strength Check: At 11.14 km, the path loss is calculated as:
  32.44+20log⁡10(11.14)+20log⁡10(430)
  20log⁡10(11.14)≈20×1.047≈20.94

  , and

  20log⁡10(430)≈52.6772

  , so:
  Path Loss≈32.44+20.94+52.6772≈106.0572 dB
  Received power

  Pr=37−106.0572≈−69.0572 dBm

  , which is well above -120 dBm, so signal strength is not the limiting factor; the line of sight is.

Given UHF frequencies’ line-of-sight nature, the communication distance is limited to approximately 11 km, aligning with the 4/3 earth radius model, which accounts for slight atmospheric refraction.

Table: Summary of Calculations

Scenario	Frequency (MHz)	Receiver Sensitivity (dBm)	Limiting Factor	Distance (km)
Flat Earth	430	-120	Signal Strength	~3900
Real Earth	430	-120	Line of Sight (4/3)	~11

Additional Considerations

• Frequency Choice: The choice of 430 MHz is based on common UHF amateur radio frequencies, supported by 5-watt UHF radio details.
• Receiver Sensitivity: Confirmed through searches that -120 dBm is typical for UHF radios, ensuring the calculation’s validity UHF radio sensitivity.
• Curvature Impact: The significant drop from 3900 km to 11 km highlights how earth’s curvature restricts UHF radio range, which is surprising for laymen expecting longer ranges.

This analysis ensures all details from the problem are addressed, providing a complete and self-contained response.

[Radioguy7268]

Yeah - the -120 dBm of the assumed average receiver is the true limiting factor.

Google up EME (earth moon earth) contests - people using the moon to bounce/reflect signals. I've heard of people making it with 2 watts or less, but they're jacking up the receivers with all types of high end pre-amps and using CW.  Voice would be problematic.

There are real world receivers out there in UHF radios (Think DMR Digital Vertex EVX & Moto XPR's) that will go down to -125 without spending too much money (and still have decent selectivity).  Those radio on a chip direct conversion receivers all the CCR folks love have some wild receive sensitivity, but they're also about as selective as a drunken politician spending someone else's tax dollars.

The original Apollo comm's with the moon were all UHF with Yagi antennas. People still heard "One giant step for mankind" although how clear it was is debatable. Then again, those Flat Earther's would point to the limitations of UHF radio signals as proof that the landing did not take place on the actual moon.

AI makes my eyes hurt.

[SteveShannon]

2 minutes ago, HHD1 said:

Let's say 2 six foot tall people with 5 watt HT's, standing on a flat earth. No trees or buildings or anything between them but air. (think fresh flatworld on Minecraft).. lol

So, same elevation. No obstructions. No earth curvature. How many fars do you think two 5-watt HT's could communicate?

Then consider with curvature.

This is just for fun.  Let's not get crazy with each other.  I just like Hypothetical discussions with friends.

WSHD560, clear and monitoring.

For the first situation it depends on the sensitivity of the receivers and the gain and pattern of the antennas, but with Yagi antennas you might easily get a couple hundred miles. 
With our earth’s curvature it’s down to about 15% farther away than the optical horizon.

[tweiss3]

Assuming unity antennas, 2 HTs at 5W, and a received signal of -110dbm, that appears to be free loss in the range of 455km (283 miles) theoretically. 

Counting curvature of the earth, and using simplified equations for RF line of site from the NOFIG manual, you are just shy of 7 miles, this ignores wattage as a factor.

 

This is all without any obstructions, like the middle of the desert. Outside factors really chop into those theoretical numbers.

[HHD1]

I could easily google this, but what's the fun in that.

I wonder if radio waves travel further in the absence of atmosphere, like space.  Or maybe it doesn't matter.

[SteveShannon]

3 minutes ago, HHD1 said:

I could easily google this, but what's the fun in that.

I wonder if radio waves travel further in the absence of atmosphere, like space.  Or maybe it doesn't matter.

They do slightly, and moisture or particles in the atmosphere can increase attenuation, but the main reason distance matters is because the radio waves become less dense as they occupy more area. Higher gain antennas minimize that.

[tweiss3]

I'll argue the -120 dbm number. Yes, that is the squelch spec for almost every radio now, but you can't understand anything at that signal strength, -110 dbm is the bottom end of what a trained ear can claim to understand.

 

Either way, theoretical flat earth is nearly nothing compared to real life experiences. 

[HHD1]

1 hour ago, OffRoaderX said:

- you are all now obsolete because it totally out-dorked all of you.

 

You weren't kidding...   And I read most of it.  It kinda sucked me into a dork vortex.  And I liked it...

[WRTC928]

1 hour ago, SteveShannon said:

 moisture or particles in the atmosphere can increase attenuation, 

The "book answer" is that moisture and precipitation have little effect on VHF and UHF signals, but I've definitely observed that it can happen sometimes. A few days ago, we had very heavy fog and drizzling rain and I couldn't get through to my usual repeater 20 miles away with a HT. Even with the base unit, I had to punch it up from 12 watts to 20 to be understood clearly. That's the first time I've had that happen, but it wasn't the first time we've had fog and rain around here, so there must be some "perfect storm" of conditions to make VHF/UHF noticeably attenuate due to precipitation. The problem with "book answers" is that my radios didn't read the book.

[SteveShannon]

27 minutes ago, WRTC928 said:

The "book answer" is that moisture and precipitation have little effect on VHF and UHF signals, but I've definitely observed that it can happen sometimes. A few days ago, we had very heavy fog and drizzling rain and I couldn't get through to my usual repeater 20 miles away with a HT. Even with the base unit, I had to punch it up from 12 watts to 20 to be understood clearly. That's the first time I've had that happen, but it wasn't the first time we've had fog and rain around here, so there must be some "perfect storm" of conditions to make VHF/UHF noticeably attenuate due to precipitation. The problem with "book answers" is that my radios didn't read the book.

I found numerous articles about humidity and various forms of precipitation affecting UHF. It definitely happens, plus the effect of varying air density as a result of temperature can cause refraction. My old satellite system used to lose its signal whenever we had heavy wet snowfall (even without snow building up on the dish and horn.)

[Radioguy7268]

2 hours ago, tweiss3 said:

I'll argue the -120 dbm number. Yes, that is the squelch spec for almost every radio now, but you can't understand anything at that signal strength, -110 dbm is the bottom end of what a trained ear can claim to understand.

Search up the Rodinia 2.3 chip used on some EVX & XPR Gen2 radios.  That is a 12dB SiNaD reading I'm quoting for that  -120 dBm - and it's easily achieved with those Rodinia receivers.  Fully quiet at -120 dBm. 

I'll agree that real world factors play into this stuff. Noise floor is the killer in most urban environments. There's a ton of trash and hash out there in the real world. Nobody is designing a commercial system around the theoretical basement level of what receivers can do.

Previous forum discussion on Receiver design