In Naval SITREP #17 (Oct ‘99), we published a detailed mathematical description of the radar model used in computer Harpoon 4. With a machine doing all the heavy lifting, we can get realistic radar detection ranges by using the actual radar equation.
For the manual game, that type of detail is simply impossible. Still, as we studied the way radar works, we got a little smarter, and have found a few refinements that we can add to the manual game without slowing play. As a matter of fact, the rules for radar get simpler. What really changes is the way we figure out what the radar ranges should be. We’re documenting it here so that players can understand why the ranges in High Tide will be slightly different than in the Harpoon 4.1 annexes, and also so they can add radars to the game themselves (or more likely, check our math).
What we used to do:
Radar detection depends on almost a dozen variables. We’ve always concentrated on the relationship between a radar’s detection range and the size of the potential contact.
All other things being equal, any radar will detect a large target farther away than a small target. Because the radar signal spreads as it moves away from the antenna, and the echo spreads again on its way from the contact back to the antenna, there is a “fourth power” relationship between radar contact sizes and their detection range.
Example: A contact with a 2 m 2 RCS is detected at 100 nm. If we increase the size of the contact to 32 m 2 (sixteen times as large), the contact is detected at (32/2)1/4 = 2, or twice as far away.
Using this principle, we set up five standard radar signatures:
| Contact Size | RCS | Sample Range |
|---|---|---|
| Large | 100 m 2 | 100 nm |
| Medium | 20 m 2 | 62 nm |
| Small | 5 m 2 | 40 nm |
| Very Small | .1 m 2 | 18 nm |
| Stealthy | .01 m 2 | 10 nm |
Note that although the medium size signature is five times smaller than a large signature, the range only drops by 38%. This is the result of the fourth power rule.
What we’re changing:
First, we’re changing the standard RCS sizes. We were overrating the signatures, and we’re also (finally) recognizing that a large ship and a large aircraft do not have the same radar cross-section (Hint: ships are bigger - much bigger). The new values are:
From now on, we’ll calculate air search radar ranges using a standard air target. Surface search radar ranges will be calculated using the standard surface target.
Second, we’re adding a new limit on the detection range of a radar. All radars send out pulses of energy, then listen for an echo. They can only listen until they send out the next pulse, so the time between pulses, translated into an out and back distance at the speed of light, becomes the upper limit on a radar’s range.
The number of pulses a radar sends out each second is called the Pulse Repetition Frequency, and is typically 200 -2000 pps (pulses per second) for a naval search radar. If it’s 1000 pps, that means the gap is 1/1000 th of a second. During that time the signal has to go out, bounce, and return. At 186,000 miles per second, the signal can cover at most (186,000/1000)/2 = 83 miles = 73 nm. This is R max , or maximum unambiguous range. It’s called “unambiguous” because the echo can only be from that signal and the time of transmission is known. It’s also called the “instrumented range.”
Example: An SPS-29 has a PRF of 300 pps. This means the maximum range it can detect a target at is (186,000/ 300)/2 = 310 miles, or an R max of 273 nm. The SPS-29’s range against a Large target is 243 nm, so the what’s the problem?
Example: An LN-66/SP radar has a PRF of 2000 pps. This works out to an R max of (186,000/2,000)/2 = 46.5 nm. But based on its signal strength, it has a detection range of 51 nm against a large target. Its detection ranges (based on signal strength alone) are:
- Large 51
Medium 28
Small 16
VSmall 9
Stealthy 5
The Rmax (Instrumented Range) limits that detection to:
- Large 46
Medium 28
Small 16
VSmall 9
Stealthy 5
Why not just leave a long time between signals? That way there’d be time for a distant echo to reach the antenna. The designers of a radar want to get as many signals out as possible, because detection isn’t certain on any one signal, especially at maximum detection range, which is where you really need to see the contact. The more echoes, the better a chance of the operator seeing the contact as soon as possible.
So they take into account the expected contact type and time the PRF to that optimal detection range. A Canadian LN-66HP is a surface ship surface search radar. It can’t see over the horizon no matter how strong the signal is, so longer detection range doesn’t do it any good. The high PRF and high signal strength means that when medium and larger-sized contacts come over the horizon, they will be picked up quickly.
If you are checking the ranges in Annex J, or researching a radar not covered by the rules, look for “instrumented range” as well as a range against a target of a stated size.
Third, we have to change the envelopes for some of the radar types. Here is a complete list of all types and what they detect: (All ranges are limited by the radar horizon. For detection, VLow is considered part of the Low altitude band)
Surface radar types:
- SS - Surface Search
Surface - at full range
Air - VLow altitude only at half listed Surf range
AS - Air Search
Surface - at 10% of listed Air range
VLow at 10% of listed air range
Air - Low and higher altitudes at listed range
HF - Height Finder
Surface - None
Air - All altitudes at listed range
3D - Three-Dimensional Air Search
Surface - at 10% of listed Air range
Air - All altitudes at listed range
Airborne radar types:
- SS - Surface Search
Surface - at full range
AS - Air Search
Air - Full range co-altitude, two higher, one lower
Half range elsewhere
AI- Specialized airborne AS radar
Air - Full range co-altitude, one higher, one lower
Half range elsewhere
Also functions as FC radar.
LD/SD - Look Down/Shoot Down (more capable AI)
Air - Full range co-altitude, two higher, two lower
Half range elsewhere
Also functions as FC radar.
RO - Range Only
No search capability, but must be used for radar-guided weapons control
TF - Terrain Following
No search capability, but must be on for NOE flight at night or in bad weather.
Changes include a revised range for detection of air contacts by SS radars, and residual SS capability has been removed for airborne AS radars. If a radar has SS capability, it will be listed separately in Annex L.
SS capability has also been removed for AI radars. If it has a SS mode, it will be listed separately in Annex L Altitudes were corrected for Airborne AS radar.
Fourth, the rules change for radar detection chances. Don’t bother rolling detection anymore, It’s not worth the trouble. After doing the math, the chance per pulse of detection quickly drives radar detection probabilities into the high nineties. This matches US Navy operational practice. If you’re in range, assume you’re detected, because you almost certainly are.
Finally, as might be expected, a thorough scrub of the radar annexes (J1, J2, and L) has revealed a lot of new data, especially for the Russians. More Soviet/Russian designations are available, allowing us to correlate them with their NATO nicknames. And of course more performance data is available as well.
We’ve also found a lot of conflicting data. That’s taken a while to sort out, and we ended up having to make a choice. There are several excellent Russian sources available now, and where we‘ve had to choose, we‘ve gone with them. High Tide, which will be out this summer, will have revised Annexes J1, J2, and L that use the new standard contact sizes and the new limit on maximum radar range.
Bibliography
Radar Evaluation Handbook, Barton, Dr. David K., Artech House, 1991
Jane’s Weapons Systems series
Jane’s Radar and Electronic Warfare series
Smarter (and Simpler) Radar Harpoon 4
BT
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