Lesson 32 Flashcards

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1. Why is a threat ring on a planning chart not really a circle?

Because the circle is one special case: one radar's detection range at one aspect (usually nose-on), at an altitude where the Earth does not block the line of sight, against a missile shot at a target flying straight at the site. Your heading changes the aspect the radar sees at every bearing, your altitude brings in the horizon, and what you do after launch changes the missile's reach.

2. An aircraft on heading \(\psi\) sits at bearing \(\varphi\) from a radar. What aspect does the radar see?

\(\theta = \mathrm{wrap}(\varphi + 180^\circ - \psi)\), measured clockwise from the nose. From the aircraft the radar lies at bearing \(\varphi + 180^\circ\); subtracting the heading measures that from the nose. \(\theta = 0^\circ\) is nose-on, \(180^\circ\) tail-on.

3. Write the aspect-dependent detection contour.

\(R(\varphi) = R_\text{ref}\,[\sigma_b(\theta(\varphi))/\sigma_\text{ref}]^{1/4}\): the R⁴ law evaluated, bearing by bearing, at the aspect that bearing produces, with \(\sigma_b\) read from the signature pattern in the radar's band.

4. On one contour, which quantity is the same everywhere and which one changes?

The heading is the same everywhere; only the bearing from the radar changes, and the bearing alone decides which face the radar sees — nose-on upstream of the site on your track, the beam abeam of it, the tail past it.

5. What shape is the flying wing's X-band contour against Project 3's TTR, and why?

An X: a ragged core about 25 km in radius (24.4 km nose-on, 25.5 km at the beams, 24.3 km at the tail) and four thin spikes out to 164.3 km at ±40° and ±140° off the nose. At X-band shaping works, and planform alignment piles the energy into four narrow lobes along the edge normals — the leading edges at ±40°, the trailing edges at ±140° — leaving every other aspect on the −25 dBsm speckle floor. (The Final Project's B-21 flies this same pattern.)

6. Why is the VHF contour nearly a circle?

At VHF the airframe's features are comparable to the wavelength (the resonance region), so shaping cannot steer the echo: the pattern moves only about 2 dB (+3 to +5 dBsm) around the compass, and the fourth root turns 2 dB into about a 12% change in range (89.9 to 100.9 km).

7. Why can routing on the nose-on ring alone mislead you?

It is honest only where the pattern sits on its floor. For the flying wing the 24.4 km ring follows the X-band core, but along the four spike bearings (±40° and ±140° off the nose) the contour runs out to 164.3 km, over six times farther. A route planned to skirt the nose-on ring can be detected much earlier than planned if it puts a site on a spike bearing.

8. State the two-ended radar horizon and its units.

\(d = 4.12\left(\sqrt{h_r} + \sqrt{h_t}\right)\) km with \(h_r\) (radar mast) and \(h_t\) (aircraft altitude) in meters, using the 4/3-Earth refraction allowance. L11's one-ended \(4.12\sqrt{h}\) is one of the two terms.

9. How do the horizon and the R⁴ law combine?

Detection needs both an echo strong enough and a line of sight, so the effective range is the smaller: \(R_\text{eff}(\varphi) = \min(R(\varphi), d)\). The two bounds never add.

10. At what altitude does the horizon stop binding?

Where \(d = R\): \(h^\ast = (R/4.12 - \sqrt{h_r})^2\). Below it the Earth sets detection; above it the signature does. For the VHF EWR on a 10 m mast seeing the flying wing nose-on at 89.9 km, \(h^\ast \approx 349\) m: at 150 m the horizon (63.5 km) binds, at 600 m the R⁴ law does. Against the TTR, which sees the wing nose-on at only 24.4 km, it falls to about 7.7 m — the quieter you are, the lower it falls.

11. Why do low observability and low altitude interact?

A stealthier signature shortens the R⁴ ranges, which lowers the crossing altitude \(h^\ast\): the quieter you are, the lower you must fly before the horizon adds anything. Terrain-following buys most against the long-range, low-band layers and little against a TTR that already sees you late.

12. Define the MEZ and the LEZ in the constant-speed model.

MEZ: the reach against a target flying straight at the site, \(R_\text{MEZ} = (v_m + v_t)\,t_\text{max}\). LEZ (the lethal or no-escape zone): the reach against a target that turns directly away, \(R_\text{LEZ} = (v_m - v_t)\,t_\text{max}\). It is a teaching model — real envelopes come from fly-out models.

13. What does turning directly away do between the LEZ and the MEZ, and inside the LEZ?

Between the rings the turn escapes: the missile must chase at \(v_m - v_t\) and runs out of flight time. Inside the LEZ even a fleeing target is caught — no escape. The turn costs progress toward the target and shows the radar your tail.

14. What is the heading-dependent envelope, and what angle does it use?

\(R(\alpha) \approx (v_m + v_t\cos\alpha)\,t_\text{max}\), the radial approximation, with \(\alpha\) the angle between your velocity and the direction to the site — the same angle as the aspect \(\theta\). It gives the MEZ at \(0^\circ\), the LEZ at \(180^\circ\), and \(v_m t_\text{max}\) abeam.

15. What is a site's lethal zone, and what sets the first shot for the flying wing at altitude?

Inside the tracking radar's effective contour, inside the missile envelope, and outside the minimum range \(R_\text{min}\). Nose-on against the TTR the track starts at 24.4 km inside a 50 km MEZ, so the track — not the missile — sets the first shot.

16. Define an overlap, a gap and a seam in a layered laydown.

Overlap: a point inside two or more lethal zones. Gap: inside early-warning coverage but outside every lethal zone — seen, not shot. Seam: the boundary where one site's coverage hands off to the next, where tracks drop and cues arrive late. All three are heading-dependent.

17. Why does a gap between two SAMs change when you change heading?

Both halves of each lethal zone depend on heading: the TTR contour through the aspect's \(\sigma\), and the missile envelope through \(\cos\alpha\). In the lesson's laydown the flying wing's gap is 49.0 km at 090°, 51.3 km at 000° and 45.4 km at 045° — but only 20.0 km at 040°, where both front sites look straight down a spike of the X-band pattern.

18. In Joint doctrine, what is a "missile engagement zone," and how does this course use the term?

In Joint doctrine (JP 3-01; the DoD Dictionary) it is airspace in which engagement responsibility rests with surface-to-air missiles — an airspace-control measure. Threat analysis and mission planning borrow the letters for a site's kinematic reach, which is the sense used here; air-to-air literature calls the inner zone the no-escape zone.