The AIM-7 Sparrow: Loft Performance [Part II]

AIM-7 Sparrow: Table of Contents

Part I: Unsung Hero: The AIM-7 Sparrow [Part I]
Part II: Loft Performance [Part II]
Part III: Range, Geometry, Phoenix [Part III]

Testing Scenarios and Caveats

About a thousand datapoints have been collected, but only half of them made it to the evaluation. The scenarios varied from dead ahead (“Hot”) at a variety of ranges and altitudes, to a flanking scenario (~25TA, 25ATA on collision – not really flanking, but it helps to differentiate the test cases).
The SAI was used to determine the pitch for the loft trajectory tests. Increasing the pitch causes an increase in altitude, at the cost of a marginal decrease in speed. The climb started at 1nm before launch for 10° and 20°, 1.5nm before launch at 30° and greater.
“No Loft” scenarios for the AIM-7P are triggered by raising the ACM cover. This operation also changes the time before release to about 1″; thus the missile is supported for slightly less long. This scenario is absent from the 7F test series, as the standard release does not loft. From this perspective, the two scenarios, STD 7F and No Loft 7P are very similar, besides the effect on the release time caused by the ACM cover.
Some scenarios were impractical or impossible, such as 50° loft at 5nm or 10nm, so I skipped them.
The tests of different launch speeds make a direct comparison of the Distance at F-Pole less meaningful, as the range decrease faster for the faster test aircraft. Absolute and relative differences offer more meaningful information.

Modus Operandi

The scenarios described above, along additional variants, are then run multiple times, the average of the results is then used to fill tables such as the following.
The data collected varies depending on the scope of the test.

AIM-7P, HOT, Speed at Impact, 25,000ft.

SPD	5nm	10nm	15nm	20nm	25nm	30nm
7P Standard	1353	1152	836	651	557	516
7P 30° Loft	1287	1228	945	754	650	589
7P No Loft	1380	1169	794	558

AIM-7P, HOT, Range at Impact, 25,000ft.

RNG	5nm	10nm	15nm	20nm	25nm	30nm
7P Standard	1.60	3.70	5.05	5.90	6.10	6.05
7P 30° Loft	1.80	4.00	5.70	7.20	8.55	9.40
7P No Loft	1.80	4.0	5.50	5.90

AIM-7F, HOT, Speed at Impact, 25,000ft.

SPD	5nm	10nm	15nm	20nm	25nm	30nm
7F Standard	1376	1197	817	564	447
7F 30° Loft	1352	1207	856	633	520	459

AIM-7F, HOT, Range at Impact, 25,000ft.

RNG	5nm	10nm	15nm	20nm	25nm	30nm
7F Standard	1.70	3.90	5.40	5.90	5.10
7F 30° Loft	1.90	3.90	5.85	6.80	7.33	7.15

The results were then computed to evaluate four aspects of the missile performance:

Speed at Impact: the idea is that the faster the missile impacts, the more energy it has, and it is more dangerous. However, focusing only on this aspect does not tell the full story;
Distance at Impact: this parameter is used as both to evaluate the trajectory / kinetic performance of the missile.
For example, a slower terminal speed but a longer range impact may suggest, depending on the scenario, a more flat trajectory, as loft envelops tend to reach the target faster but also require more time. These aspects are severely linked to the altitude, as a flat trajectory “suffers” more at lower altitude. Understanding these sorts of considerations is key to employ the AIM-7, and any missile, really, in the most efficient way.
Absolute and Relative relations: As we will see, often a higher pitch angle results in greater range and speed at impact but, after a certain angle, it becomes to assess the actual gain.
The Absolute ratio expresses the gain, or loss, compared to the standard employment method. The Relative ratio instead compares a certain value with its predecessor, to determine, simply put, whether the effort is worth or not. For instance, pushing to 40%+ pitch angle can be fundamental in some cases, in other it can be the opposite. On top of that, such a severe angle can cause issues in terms of loss of SA, formation integrity, visual awareness and so on. All these aspects should be considered besides the raw numbers.

The charts are organised in a 4×4 matrix. The left column is the speed, the right column is the distance.
Click on a chart to open a greater resultion version in a new tab.

Loft Characteristics: Study

The first series of tests dives into the loft properties of the AIM-7. Not only the self-lofting 7P and 7MH, but also the 7F when properly “invited” to raise to the heavens.

Standard Scenario

The first block of results is set in the following scenario:

SPD_F14: M.9 and M1.1;
SPD_TGT: M.8;
ALT_F14: 25,000ft and 10,000ft;
ALT_TGT: 25,000ft and 10,000ft;
SR: 25nm and 10nm;
Geometry: TA=ATA=0.

25,000 ft; 25nm; Hot

OBSERVATIONS

This is the simplest scenario, co-alt and head-on. The range is quite important, 25nm.
Starting from the speed, it is noticeable how lofting improves the final result, for both the AIM-7P and the AIM-7F. The 7F unfortunately does not reach the target faster than M1.0, making it a very low threat, but it still forces the target to take action, even just by cranking. The 7P becomes instead a much greater threat but, interestingly, the benefits wind down after the loft angle passes 30° and becomes counterproductive after 40°. Possibly, when the angle reaches 50°, the missile invests almost too much energy climbing, and the trade does not pay well speed-wise.
The distance at impact sees an even greater gain, and the benefit is almost linear across the results. This may surprise new players that do not expect such a gain in terms of range. In fact, one of my first PvP kills in the F-14 with the Sparrow was an AIM-7M thrown at a hot human Su-27 from about 25nm.

Takeaway points

7P: at considerable distances and medium altitude, high loft angles make a tangible impact until the pitch angle is greater than the distance itself. The gain in terms of distance is significant.
7F: this is not a missile efficient at long range. The lack of self-induced loft makes it entirely dependent on the actions of the pilot loft. It can perhaps work against a non-aware, non-manoeuvring target, but otherwise better reduce the range before employing.

25,000 ft; 10nm; Hot

OBSERVATIONS

At the same altitude but at much shorter range, both versions of the Sparrow perform well. The questions are more about if and how lofting is beneficial.
In terms of speed, it appears it is better to either force the AIM-7P to avoid the loft, or force a less pronounced loft, than employing without it or push the angle too much. In fact, even when there is a gain, the magnitude is about ±2%. The 7F fares similarly, but lofting actually tends to degrade the speed at impact.
Range-wise, the no-loft option for the 7P seems to be the most efficient overall, and although the 40°/50° pitch provides some gains, we are talking about half a mile at best, at the risk of losing the lock: at such angles in fact, if the target dives quickly and manoeuvres, it may suddenly move outside the gimbal limits.

Takeaway points

7P and 7F: although lofting slightly improve the distance at impact, the difference is negligible for both missiles. At medium altitude and short range, the no-loft option (or standard delivery, in case of the 7F) is a solid solution.

10,000 ft; 10nm; Hot

OBSERVATIONS

Low altitude immediately affects the performance of the AIM-7 by a solid 200/300 kts. Even at short range.
Although the behaviour overall seems quite similar compared with the previous scenario, the loss of speed and distance at impact is noticeable.
The chart describing the speed changes is quite interesting: the no-loft option actually degrades the performance, and a slight pitch up of 10°/20° brings minor advantages for both missiles in terms of speed. On the contrary, the distance benefits almost linearly from the induced loft, although we quickly enter the realm of the diminishing returns.

Takeaway points

7P and 7F: both versions behave similarly, and are both affected by the thicker air of the lower altitudes. A slight pitch can be beneficial here, but it is definitely not a must-do.

10,000 ft; 25nm; Hot

OBSERVATIONS

This scenario is tough for any missile, whether an AIM-120, an AIM-54 or an AIM-7 is launched. Therefore, this is a shot that should not be taken unless necessary.
On the other hand, this scenario gives an idea of the performance loss at low altitude as the range increases, and how the self-induced loft trajectory used by the 7P helps to compensate such inefficient parameters. This should help you decide, in non-restricted scenarios, whether you should take a “non-lofting” AIM-7M, or an AIM-7MH or 7P.
Speed-wise, there is not much to say. For the 7P is surprisingly fairly constant, but the 7F sees drastic gains. The distance at impact is more meaningful, more than doubling the value, but the point stands: this is not a short worth taking.

Takeaway points

7P: interestingly, the loft does not affect the speed at impact much, but it skyrockets the distance at impact, doubling it. Although a shot may still connect, it is a very low P_K one. Only a non-aware, non-manoeuvring target may be threatened. Saving the shot and reducing the range sounds like the best course of actions.
7F: although the 7F benefits from the loft in a very noticeable way, save the short and reduce range. Its speed at F-pole makes any marginal change in TA capable of kinetically defeating the Sparrow, despite the good geometry.

Speed Differences

The second series of tests changes the speed of the F-14 whilst maintaining the same shuffle of altitudes and distances.
The missile version compared is the 7P.

25,000 ft; 25nm; Hot; Speed difference (M1.1)

In the original setup, the No Loft option was a no-go. Despite the slight speed advantage, it is not feasible at M1.1 either.
Speed-wise, compared to M.9, the behaviour is still very similar, but the loft performance looks smoother.
The distance cannot really be compared directly, as the faster aircraft is closing distances sooner than the slower, but we can notice how the additional energy provided to the missile by the increasing loft is invested in altitude, allowing the missile to reach the apex with more energy, thus impacting the target sooner. The gain in distance as the pitch increases, in fact, is almost linear.

Takeaway points

7P: “Every little helps“. The energy is invested into a more efficient loft, allowing the missile to hit farther and sooner, providing greater dividends.

25,000 ft; 10nm; Hot; Speed difference (M1.1)

Probably due to the shorter range, the behaviour of the missile is almost unchanged, both in speed and distance at impact. The speed curve is simply offset up, and the same considerations apply.

10,000 ft; 10nm; Hot; Speed difference (M1.1)

Same as above, the behaviour is still very similar when the speed change is not huge.

10,000 ft; 25nm; Hot; Speed difference (M1.1)

This scenario is definitely more interesting. Although the missile is launched faster, the impact speed is still quite the same, and still insufficient to pose a threat. In the other situations, instead, a greater speed at launch directly translated into a greater speed at impact. Here, this is not the case.
The faster employment instead greatly increases the distance at impact by more than 300%: employing, and cranking and slowing down should ensure a good separation at F-pole (“good” compared to the standard scenario, of course).
Still, this is not a shot worth taking, if not in particular situations.

Takeaway points

7P: at low altitude and long range, flying faster does not help the missile as much as expected.
The F-14 is actually faster than the AIM-7 as the rocket motor runs out.

Altitude Difference

The F-14 Tomcat likes staying up, especially with the new AIM-54. This scenario tests what happens when the target is 15,000ft lower than the launching aircraft.

25,000 ft (F-14), 10,000ft (TGT); 25nm; Hot

(Compared to co-alt, 25,000ft, 25nm.)

At long range, a solid loft helps the missile to preserve its speed at impact, but a slight loss is noticeable, as the AIM-7 has to dive through the atmosphere, where the air offers greater friction.
If we consider only the speed, the climb advantage is negligible. When considering the distance advantage instead, there is a very visible gain. Even more surprisingly, the gain is almost linear.
Although such a long shot may not worth it overall, if necessary, increasing the loft can still be worth it.

Takeaway points

7P: increasing the loft onto a lower target does not provide the same benefit in terms of speed at F-Pole it shows in a co-alt scenario. On the other hand, it marginally increases separation at impact, but not in a particularly substantial way.

25,000 ft (F-14), 10,000ft (TGT); 10nm; Hot

(Compared to co-alt, 25,000ft, 10nm.)

The conclusions of this scenario are probably easy to guess: at such a short range, adding loft means that the missile bleeds energy changing trajectory from upwards, to downwards as it suddenly dives down. This is reflected by the speed of the AIM-7 at the impact that diverges from the standard employment already discussed. It is even more visible in the absolute and relative comparisons: any option besides Standard employment and No Loft generates negative results.
In terms of distance at impact, the previous scenario, ΔALT at longer ranges, saw benefits in terms of distance at impact. At 10nm those are negligible and are probably not worth it, in light of the observations about the speed.

Takeaway points

7P: since the gain in distance is minimal and lofting introduce negative results, better stick to default or no loft.

10,000 ft (F-14), 25,000ft (TGT); 25nm; Hot

(Compared to co-alt, 10,000ft, 25nm.)

This test reverses the scenario, and the F-14 is now lower than the target. Intuitively, higher pitch and loft favours the Sparrow, the question is determining how much this choice impacts the results.
Speed-wise, the gain is not irrelevant. The missile is probably still too slow to be a threat, but compared to the 10,000ft, 25nm scenario, it is not that bad either. In fact, interestingly, as the loft increases, the missile tends to climb higher than the target and then dive, whilst lower pitch angles cause the missile to level before impact. By outclimbing the target, the missile can trade altitude for speed, something it cannot do if it is too slow to place itself in such a position.
In terms of distance at F-pole, the gain is very noticeable, and on-par with the standard, employment.
Overall, this is a shot not worth taking, if possible, as the combination of range and thicker air cause severely impact the AIM-7 performance.

Takeaway points

7P: at long range, when the F-14 is lower than the target, drastically increasing the loft bears tangible results. Still, the missile does not have enough energy to be a threat versus any aware or manoeuvring target.

10,000 ft (F-14), 25,000ft (TGT); 10nm; Hot

(Compared to co-alt, 10,000ft, 10nm.)

At considerable altitude difference but much shorter range, the energy is less of a problem.
In terms of speed at impact, interestingly, the “forcibly lofted” AIM-7 ends up having better performance than the co-altitude launch. In fact, in No Loft, Standard or low-angle loft, the missile has to climb on its own to reach the target. If the pitch angle is substantial instead, not only altitude is gained during the manoeuvre, but the missile can invest more energy in improving the climb, rather than turning from the horizontal to the climb. A similar effect was observed in the previous test.
Although diminishing returns start as the angle passes 20° and the results are irrelevant or negligibly negative at 50°, this is one of the few cases where pushing the manoeuvre can be beneficial, as the fighter may want to press on, maintaining the target almost on the nose, and preparing for a follow-up FOX-2 shot (this approach leaves the door open for both a FQ and a RQ shot).
Distance-wise, albeit marginally, the shot from lower altitude arrives sooner than the co-altitude, possibly because the loft parabola generated when co-altitude is much less direct than a shot from below.

Takeaway points

7P: Possibly one of the very few cases where pushing may be worth it, if anything, to be in a better position for a follow-up shot with an AIM-9. The performance of the AIM-7 is similar to the co-alt scenario, slightly better if the Tomcat climbs at a 20°/30° angle before launching.

Recap and Conclusions

Wrapping up this first part of the numerical analysis in the shortest manner possible, we can observe that, in a “hot” scenario:

At longer ranges, “hard” loft always provide a benefit, but as the pitch passes a value close to the range, the return of investment becomes less and less tangible. The altitude is a critical parameter in this scenario;
The non-lofting Sparrows (7M, 7F and older), despite the additional energy gain created by the pilot inducing the loft, turn out to be much less effective, energy-wise, than the 7MH and 7P in the endgame, especially as the range increases;
At short range, no loft, or only a few degrees, seem to be the simplest and more effective option, unless the shot is taken at low altitude, where every bit of additional altitude can be traded for energy later;
Impact distance tends to be the aspect that gain the most from inducing a steeper trajectory.
When engaging a target lower than the F-14, the benefits provided by the loft are minimal, if not negative, both in terms of speed and distance at F-pole. On the contrary, when engaging a target higher than the fighter, the same considerations of a co-alt engagement apply. It can be argued, however, that at short range, climbing further to set up a follow-up shot can be beneficial.

Part III of this study focuses on different geometry and provides a different look at the performance of the AIM-7, concluding with a comparison with the AIM-54 Phoenix in similar scenarios.