# Physics and "Toss Bombing" **URL:** \ **Category:** Factual Questions\ **Created:** [April 28, 2023, 4:56pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319 "2023-04-28T16:56:36Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![MikeF](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@MikeF](https://boards.straightdope.com/u/MikeF)\ **Post date:** [April 28, 2023, 4:56pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/1 "2023-04-28T16:56:36Z")
In a Ukraine war thread, the use of guided/steerable bombs (JDAMs) was discussed. One way to deliver this weapons is to speed along close to the ground, pull up abruptly and release the weapon. (Presumably, at or near the top of the climb). The bomber then dives while reversing course (half Cuban 8). This to minimize exposure to air defenses. My question is this: what the ideal tactic for getting the most range for the “toss”, assuming there is no leveling out and regaining speed at the top of the climb? Isn’t the energy the same for a fast, low release as a slow, higher release? Aside from the physics, what other real-world factors come into play? Do the inertia guidance systems work better at a steeper angle? I assume Max range and max accuracy are in opposition but I may be wrong about that. In other words, maybe once the accuracy is down to single digits in meters, getting closer at the expense of greater risk of being shot down isn’t worth it. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [April 28, 2023, 5:23pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/2 "2023-04-28T17:23:00Z")
Questions of accuracy are largely superceded with terminally-guided munitions like JDAM. Get the weapon pointed in the right direction with enough altitute and speed, and the wings and the GPS receiver take care of the rest. For unguided toss bombing, it will be less accurate than dive bombing or other kinds of bombing where you sight the target and can adjust for last minute variables, but it’s still more effective than a bomb that never gets dropped because the aircraft was shot down before delivering. ---
**Author:** ![bump](https://avatars.discourse-cdn.com/v4/letter/b/7c8e57/32.png) [@bump](https://boards.straightdope.com/u/bump)\ **Post date:** [April 28, 2023, 7:51pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/3 "2023-04-28T19:51:36Z")
I think the point behind JDAMs and other terminally-guided munitions is that they’re essentially independent of the delivery aircraft. Toss-bombing was developed for nuclear weapon delivery, IIRC. So the whole point was that toss bombing could get the bomb close enough, while being released from far further away than otherwise, thereby saving the pilots from the effects. With modern day precision guided conventional bombs, the idea would be that they can release from further away and still hit the target accurately, thereby reducing AA exposure. I suspect there’s more than likely some sort of technique that pilots are taught in just _how_ to go about toss bombing- so many knots in a shallow dive starting at Y altitude, pull up into such an angle of attack X many kilometers from the target, release at some point, etc… so that they can put bombs near the target in a repeatable fashion. Once that’s done, the GPS guidance takes over, or in the case of something like a Paveway, the seeker starts looking for the laser designation, and homes in on the target. As long as the bomb is within some distance from the target, the guidance can compensate and hit the target. The actual toss-bombing technique and the particulars of altitude, distance, speed, etc… are probably particular to the bomb itself- size, guidance mechanism, etc… A 2000 lb Paveway is going to be a different beast than a 250 lb SDB. ---
**Author:** ![MikeF](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@MikeF](https://boards.straightdope.com/u/MikeF)\ **Post date:** [April 29, 2023, 12:35pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/4 "2023-04-29T12:35:55Z")
While both of the replies make sense, they don’t really answer the question about getting maximum range from a toss. A little research shows that that this is achieved by releasing while climbing at 32 degrees and is independent of the weight of the object. Of course the greater the release altitude, the greater the range This is in a vacuum so drag is not a factor. My limited grasp of aerodynamics (gained from being a glider pilot) informs me that there is an ideal speed when it comes to maximum glide range and this would impact the JDAMs with wings. According to Wikipedia. the maximum ranged of the winged JDAM is 80 km but it doesn’t say what the release altitude would have to be to achieve this. Finally from Wiki, “In its most accurate mode, the JDAM system will provide a minimum weapon accuracy CEP of 16 feet (5 m) or less when a GPS signal is available. If the GPS signal is jammed or lost, the JDAM can still achieve a 98-foot (30 m) CEP or less for free flight times up to 100 seconds” In any case, the video showing the purported use of four 500 lb. (the smallest JDAM) JDAMs is pretty impressive. Maybe Ukraine is saving its supply of these weapons until they will have the maximum impact. Pun (sort of) intended. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [April 29, 2023, 2:08pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/5 "2023-04-29T14:08:15Z")
Don’t forget that unlike a glider, a powerful modern fighter-bomber won’t necessarily lose much speed in the climb. So the trade off you assume (low-fast vs high-slow) may not exist to the degree you think. ---
**Author:** ![bump](https://avatars.discourse-cdn.com/v4/letter/b/7c8e57/32.png) [@bump](https://boards.straightdope.com/u/bump)\ **Post date:** [April 29, 2023, 10:48pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/6 "2023-04-29T22:48:33Z")
I would imagine the whole point would be to gain a certain amount of speed (afterburners, shallow dive, etc…), then pull up to a specific angle of attack, and release when the airspeed shows a certain value, thereby optimizing the horizontal and vertical speeds. I would imagine how you get the speed to do the toss bombing would be different based on the capability of the plane to gain speed. An old Greek F-4 with a 2000 lb JDAM might need a shallow dive or afterburners, while a Eurofighter with a 500 lb JDAM might just be able to power into that climb. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 30, 2023, 4:41pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/7 "2023-04-30T16:41:43Z")
If you’re launching something at a set speed, from ground level, and neglecting air resistance and the curvature of the Earth, then 45º is optimal. But the problem isn’t that simple, because you’re not at ground level, and your speed might depend on the angle and on the height, and air resistance is almost certainly relevant, and so on. ---
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [May 1, 2023, 7:05pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/8 "2023-05-01T19:05:51Z")
for back of envelope calcs, assume slightly subsonic, say 600mph. sin or cos 45° is going to be .707 so about 424mph up and horizontal, or 622fps. How high does that go? v=at 622=32t, so t=19.4 sec up and same down; 38.8 sec at 622fps gives me 24,133 feet or about 4.5 miles. This assumes launch from ground level, trying to hit a spherical cow in a vacuum… but gives you a rough idea. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 1, 2023, 8:31pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/9 "2023-05-01T20:31:38Z")
I tried to do a little better than ground level, vacuum, and spherical cow by writing a python program to calculate furthest range and release angle for a given initial velocity and height. I assume avg seal level air density, completely ballparked the drag coefficient and avg cross sectional area of a GBU-31 (but i did find the mass online). Used basic trajectory calcs and Euler’s method for integration. My results: Enter mass (kg): 925.4 Enter drag coefficient (dimensionless): 0.11 Enter cross-sectional area (m²): 1.64 Enter initial height (m): 183 (approx 600 ft) Enter initial velocity (m/s): 269 (approx 600 mph) Enter air density (kg/m³): 1.225 Maximum range: 4718.82 m (approx 3 miles) Optimal launch angle: 40.00° ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [May 1, 2023, 8:53pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/10 "2023-05-01T20:53:49Z")
I don’t see “peak altitude” in that output. For tossing a guided glide bomb, that’s probably the most important outcome: does the weapon have enough altitude to attain the gliding range necessary to attack its target? ---
**Author:** ![MikeF](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@MikeF](https://boards.straightdope.com/u/MikeF)\ **Post date:** [May 1, 2023, 10:31pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/11 "2023-05-01T22:31:41Z")
So, what altitude is required at 600 kts to get the claimed 80km range? ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 2, 2023, 2:50am UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/12 "2023-05-02T02:50:25Z")
This calculates a ballistic trajectory. The GBU-31 JDAM is not a glide bomb. That’s an entirely different kettle of fish, since you now add wings and aerodynamics to the mix. ---
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [May 2, 2023, 4:17am UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/13 "2023-05-02T04:17:42Z")
The cessna 150 IIRC had a glide ratio about 8:1 which was supposedly quite good; assuming a glide bomb has that degree of glide, it would have to be 10 km high. This assumes unpowered, and a glider will quickly slow if it is light, but will drop too fast if it is heavy enough to mitigate drag… I doubt you can lob an unpowered subsonic bomb up 10 km. (Travelling too slow it becomes an easy target, too) ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [May 2, 2023, 2:24pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/14 "2023-05-02T14:24:41Z")
The Ukranians are using JDAM-ERs, which are winged. > **[Winged JDAM Smart Bombs Are Now Operational In Ukraine](https://www.thedrive.com/the-war-zone/winged-jdam-smart-bombs-are-now-operational-in-ukraine)** > > The U.S. Air Force's top officer in Europe says JDAM-ERs are now in Ukrainian hands, putting whole new Russian target sets at risk. Therefore, the most relevant factor is peak altitude, since the release is ballistic – the wings don’t open until after the toss has reached max height. Ballistic peak altitude is quite possibly the most important dependent variable. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 2, 2023, 2:31pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/15 "2023-05-02T14:31:59Z")
Yep, I didn’t realize they were using the winged ones at first - but like I said, calculating max gliding range of one is a much more difficult problem since we’re not (at least I’m not) privy to any of the glide characteristics. So I can approximate the max height of the ballistic trajectory from release, but nothing past that. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [May 2, 2023, 2:35pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/16 "2023-05-02T14:35:49Z")
> [@Dorjan](#): > > approximate the max height of the ballistic trajectory from release, That’s a good start. The glide characteristics can be computed (or at least guessed) from that start point. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 2, 2023, 2:43pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/17 "2023-05-02T14:43:38Z")
> [@gnoitall](#): > > That’s a good start. The glide characteristics can be computed (or at least guessed) from that start point. If I had the Lift to Drag ratio of the wing kit, sure. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 2, 2023, 2:47pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/18 "2023-05-02T14:47:48Z")
I guess I could take their word for it and go with 8:1 and go from there … ---
**Author:** ![Seren359](https://avatars.discourse-cdn.com/v4/letter/s/a87d85/32.png) [@Seren359](https://boards.straightdope.com/u/Seren359)\ **Post date:** [May 2, 2023, 5:27pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/19 "2023-05-02T17:27:34Z")
Remember, toss bombing was a tactic for delivering nuclear weapons from low-flying fast jets. It did not have to be super accurate. The 400 Kt warhead took care of that for you. It was intended to allow the delivering plane to leave and clear the blast radius. It would work with a “smart bomb” because that can correct its impact point. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [May 2, 2023, 6:02pm UTC](https://boards.straightdope.com/t/physics-and-toss-bombing/983319/20 "2023-05-02T18:02:20Z")
OK, I updated my script and I’m getting results that look reasonable. I broke the calculations down into two parts - part 1 is ballistic trajectory to calculate max height, horizontal distance traveled at max h, and forward velocity at that point. Part 2 calculates glide distance given that height h, forward velocity, and a glide ratio of 8:1. Air density is static to keep the calcs simple (1.225 kg/m^3), drag coefficient is set to 0.15 for the ballistic portion and cross sectional area of 0.164 m^2 (wings stowed). For the glide portion all that is encompassed by the glide ratio. Enter projectile mass (kg): 317 Enter initial height (m): 1828 (~6,000 ft) Enter initial velocity (m/s): 330 (~738 mph, just under Mach 1) **Optimal launch angle: 37.00°** Part 1: Max height and horizontal distance traveled at max height **Max height: 3530.50 m** Horizontal distance at max height: 4211.55 m Forward velocity at max height: 211.56 m/s Part 2: Total range **Total range: 80350.05 m** Again this is super basic and ignores other real world factors [Next page](https://boards.straightdope.com/t/physics-and-toss-bombing/983319.md?page=2)