This pretty high level of technical discussion for yours truly but I will also like to throw in my two pence.
First that the reference to Prithvi variant can mean lot of things. The AXO booster motor can also be a shorter one compared to 6m length of motor. Also on other note the reference to Prithvi variant may just be accounting jargon to justify the diversion of Prithvi funds for the AXO. So one has to be careful for taking the full length motor of 6m as basis of AXO.
On second note, I think that for logistical compatibility Drdo may look at length of 8-9m rather than 10-12 meter. Not to mention that it this missile is also supposed to be used by Navy in future as area SAM then it may need careful look at the dimensions.
I cannot comment on the burn time but if you look at AAMs then their burn time can be as low as 5-10 seconds and then they coast for another 20-40 seconds or even more.
On the other hand I think the speed of AXO will much greater than PAC-2/3 as Pranab had commented sometime back about their high reaction time and thus unsuitability for Indian scenario.
On other note if AAD vehicle is taken as basis then if we think that 3 missiles have to be mounted thereupon then the weight of whole missile may be as low as 1100-1200kg. Though in pictures it seems like only one missile on the launcher.
Even for kill stage I think we should factor in weight of explosive warhead, sensors, data links, electronics, batteries, lateral thrusters etc and take it to be atleast in the range of 500kg.
So my guess
Booster ~.70m can be 4-6 m length 1500-2500kg
Second stage ? dia can be 2-4m length 500kg
Kill stage ? dia can be 1-2m length 500kg
This DRDO's Large Size Solid Booster
when used as a single stage ABM will be approximately:
Mass: 2,700 Kg (2.5tonne booster mass + 200Kg interceptor including terminal cross thrusters)
Length: 9-10 meter
Powered Flight time:38 sec
Final velocity: Mach 11.5 (3.5Km/sec)
Minimum intercept altitude: 45Km (that is how long the booster burns before it can release the kill vehicle)
A 2-stage ABM that has 500Kg second stage will be approximately:
Mass: 2,700 Kg (2.5tonne booster + 500Kg second stage + 200Kg interceptor including terminal cross thrusters)
Length: 10.5-11.5 meter
Powered Flight time:58 sec
Final velocity: Mach 15(4.5Km/sec)
Minimum intercept altitude: 70Km (that is how long the booster burns before it can release the kill vehicle)
These numbers correspond to firing at an angle such that terminal velocity is at 45 degree elevation (this also allow reader to roughly estimate the ground imprint when payload becomes active ).
Bheri bheri different from any other missile in world.
Arun -- are you not beeing very cute/cheeky in your first sentence.. "this booster when used as".. so the numbers are (only) for the case if this booster is used as ABM. But you are not revealig if it "is used" or "if you think it is used"..
1. The flight time as 1stage ABM is 38sec from the motor specs per DRDO release.. However per some reports the interception time is 110/117 seconds.. i think it is not too comfortable for the interceptor to be un-powered for so long
(~70secs).. and with 200Kg total mass it may have very less powered flight of its own..
given that prithvi liq-fuelled Prithvi has a flight time of 300sec to reach a 150km target.. we can assume about the same or more for a solid-fuelled Prithvi (going longer range)6m long 1m dia motor..
total powered flight of it can be as low as 38sec? is that enough? (assuming 0.8m dia motor burn time will also be same as 1m dia counterpart)
2. please look at the 2-stage ABM mass calculations.. they dont add up.. You missed adding the 2nd stage mass to the total
You are right Rakall on Mass calculation.
On powered flight and non-powered one..it depends upon the situation. And for the terminal phase interceptor 70 secs unpowered flight is high.
To add..there are two ranges reported normally. One if max. range. And, other is max. range of flight. Max. range is range covered by powered flight. and max. range of flight is one including the non-powered flight time.
With that information, if you see the spec of Arrow-2, max range is 70km and max. range of flight is 90 km. With this information, if we did gross comparison, 70s non-powered flight is too high.
There is one more angle too, to show there is discrepancy in the data provided above. For stage 1.
Max. velocity is given as 3.5 km/sec. Initial velocity is 0. If we assume, uniform acceleration. Then average velocity is 1.75
km/sec. With 38 sec. duration its range is 66.5 km
.For stage 2.
Intial velocity is 3.5 km/sec(due to first stage terminal velocity) and final velocity is given as 4.5 km/sec. So average velocity is 4km/sec
(assuming uniform acceleration). For a duration of 58 secs, range convered is 232 km
Now we add the first stage range + second stage, Then total range of AXO is 298.5 km
Even if we consider, drift and change in g, and other data, this is too high compared to what is reported in the media the range as 100km
I cautioned him on using the data which appeared some 6 yrs ago. Anyway its all boils to individual opinion.