Comparison by Spurts

[garrya]

Which, as is clear from your own source, this wasn't the requirement.

I know, I'm trying to say that while the requirement is only 6:1, they actually demonstrated 9:1 with their design. In other words, the real throttle ratio excess the requirement.

[sprstdlyscottsmn]

And yet I find that with the 300s time limit 6:1 allows greater range than 10:1. I'm going to do an analysis to see what throttle ratio is best for a given intercept range.

[eloise]

And yet I find that with the 300s time limit 6:1 allows greater range than 10:1.

Isn't that obvious?
If I understand it correctly, the main reason for high throttle back ratio is to conserve fuel and increase burn time. But high throttle back ratio also mean lower minimum thrust. So if the total burn time is a constant then higher throttle back ratio will allow less range.

[marauder2048]

Which, as is clear from your own source, this wasn't the requirement.

I know, I'm trying to say that while the requirement is only 6:1, they actually demonstrated 9:1 with their design. In other words, the real throttle ratio excess the requirement.

At that point, 9:1 was a laboratory demonstration. That's where you typically see those high figures.
6:1 or maybe 7.5:1 is what's typically attainable in flight.

And yet I find that with the 300s time limit 6:1 allows greater range than 10:1.

Isn't that obvious?
If I understand it correctly, the main reason for high throttle back ratio is to conserve fuel and increase burn time. But high throttle back ratio also mean lower minimum thrust. So if the total burn time is a constant then higher throttle back ratio will allow less range.

I'm not sure how this is being modeled but a higher turndown ratio should always produce better range.
Particularly in lofts.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a257018.pdf

[sprstdlyscottsmn]

300s was a battery power limit. At 10:1 the motor was laying almost the whole time. At 6:1 the motor was burning out much sooner but the higher average speed meant it went further in 300s

[marauder2048]

300s was a battery power limit. At 10:1 the motor was laying almost the whole time. At 6:1 the motor was burning out much sooner but the higher average speed meant it went further in 300s

Quite why a missile with the putative range would rely on battery power rather than an
alternator (see PGK, SDB II) is strange.

A big gain from higher TDR is reduced overspeeding at altitude which is really important to the radome.

And the state-of-the-art for batteries 6 years ago doesn't seem like a big ask for > 300 seconds flight time.

https://www.navysbir.com/n14_2/N142-092.htm

[madrat]

Solidstate capacitor storage would better fit the role.

[marauder2048]

Solidstate capacitor storage would better fit the role.

They tend not to like the very low temperatures where external stores have to operate.

Though I suppose there's nothing preventing the weapons station from charging/heating them up
prior to launch.

[sprstdlyscottsmn]

Okay so I just ran the TDR vs time-to-range analysis.

Constants:

launch airspeed - M1.0
launch altitude - 36,000ft
target altitude - 36,000ft
target speed - M0.0 (used to control the impact point)
max electrical power - 300s
minimum powered flight speed - 1.9M (throttle will not reduce below what is needed to sustain this speed)
loft - 4 deg to a max alt of 85,000ft to feed motor enough oxygen (this alt not reached in this test before turn down to intercept)
total weight - 419lb
total fuel weight - 143lb
effective ISP - 795s
Boost - 2s @ 5600lb
Sustain - 30s @ 2662lb (TDR 1:1)
Lift Area - 4.8ft^2
Drag Area - 0.31ft^2 (zero lift)

Variables:

TDR - 1-10 in whole numbers
target impact distance (TID)

Throttle logic: When time-to-impact is less than or equal to remaining motor duration at full thrust, full thrust. Otherwise the maximum value of minimum throttle or thrust required to sustain minimum powered flight speed (as missile climbs in loft this will switch from MPFS to MinT depending on TDR.

Results by TDR:

1 - range is aero limited (stall) at 70nm, best for TID between 0 and 52nm
2 - range is aero limited (stall) at 96nm, best for TID between 52 and 73nm
3 - range is time limited at 112nm, best for TID between 73 and 93nm
4 - range is time limited at 124nm, best for TID between 93 and 111nm
5 - range is time limited at 132nm, best for TID between 111 and 127nm
6 - range is time limited at 136nm, best for TID between 127 and xxxnm
7 - range is time limited at 128nm, never best under the current time constraint
8 - range is time limited at 123nm, never best under the current time constraint, still under power at impact
9 - range is time limited at 121nm, never best under the current time constraint, still under power at impact
10 - range is time limited at 119nm, never best under the current time constraint, still under power at impact

This model was built before the above information about boost phase time and speed. Boost motor stats can be changed to reflect this and MPFS can be adjusted as well, this will reduce all ranges. Loft can be increased to extend ranges.

[marauder2048]

Okay so I just ran the TDR vs time-to-range analysis.

Is there really evidence that powered flight is possible below Mach 2?
The paper indicates Mach 2.5 is about the minimum powered flight Mach.

And Max thrust doesn't take into account the restrictions on radome heating.

While I appreciate your modeling efforts; the table above from the paper gives
the appropriate and IMHO more convincing data points.

[sprstdlyscottsmn]

You didn't read until the end did you?

This model was built before the above information about boost phase time and speed. Boost motor stats can be changed to reflect this and MPFS can be adjusted as well, this will reduce all ranges. Loft can be increased to extend ranges.

I built this flight model over about two years ago, I saw the paper you referenced yesterday. In the effort of a reduction analysis I was using my model as was and only playing with TDR. I figured you would be able to appreciate that, since I specifically addressed your concerns at the end of my post.

I don't mean to sound ungrateful, because I am very grateful for the information provided. The next thing I will be doing is updating the minimum speed to 3.0M based on the TDR 5 and TDR 10 data shown and improving the boost phase to reach 2.5M from the minimum launch conditions. I will also try to implement a maximum speed of 4.0M. If you have anything concrete about max electrical power time I will happily take that too, otherwise I will be sticking with 300s.

[sprstdlyscottsmn]

This is all coming at the perfect time because I am about the start the Typhoon, which will be the first Meteor equipped plane in the comparison.

[marauder2048]

You didn't read until the end did you?

There's really no need since the scholarly, peer-reviewed paper has actual data points.
So I don't have to trust the vagaries of your modeling which seems to have a predilection
for unsourced magic numbers.

[garrya]

There's really no need since the scholarly, peer-reviewed paper has actual data points.
So I don't have to trust the vagaries of your modeling which seems to have a predilection
for unsourced magic numbers.

Discussion about the accuracy of Spurt analysis is fine and I think it is helpful to contribute better data points that you have but that aggressive tone is uncalled for.
After all, Spurt done all this analysis and calculation by himself. Not only it takes a lot of time, he also done that for free.
A little appreciation is better.

[madrat]

There is sufficient motivation not to publish everything about a weapon system capability. Spurts gives us insight to what could be possible. In no way is he going to leak secrets just to show off here. The attack on his credibility is absurd considering you offer zero to refute his numbers. Absolutely nothing.