In the previous post about Chinese missiles and the DF-31, technical solutions utilized on Chinese missile engineering, were described.
To set it into relation, a comparison with the benchmark of solid fuel ballistic missiles is helpful.
In many ways the UGM-133 Trident II may be regarded as the best ballistic missile ever built and it is more than three decades old.
While U.S military industrial complex produced quite a number of inefficient or ineffective systems in the tactical field, strategic systems are much less affected by this. The missile segment of the U.S Navy's fleet ballistic missile program and its final product, the Trident II, is a ideal example.
The Soviet SLBM program needed to catch up in this area and roughly did so by the 70's. Their liquid fuel SLBM design school was cost-effective, compact, had high throw weight and normally did what the U.S FBM SLBM did, but with one stage less. The price Soviets had to pay were accidents, that come with having a liquid fueled missile inside a submarine, but with increasing experience it was mastered.
The U.S approach simply applied the highest performing solutions, with costs playing a lesser role, resulting in the Trident II.
How to compare?
Comparing secretive strategic weapons systems requires data and numbers, otherwise it is pure speculation.
The situation is quire difficult for the DF-31 series, but OSINT material, easily available via Google search, is more helpful for Trident II.
Physical dimensions are the main requirements to analyse the system. There are two drawings that are claimed to be (intended?) leaks: One detailed technical drawing on the Trident II and one less detailed one from an U.S intelligence briefing about the baseline DF-31.
For a rough performance assessment the following four basic parameters are needed, additional to the dimensions:
Isp of fuel/motor/nozzle combination
Density of the fuel
Percentage of aerodynamic losses of the missile (features, layouts and dimensional ratios)
Either propellant mass fraction, or structural ratio, also called deadweight ratio, for the applied technology
Reasonable estimates are necessary for this four parameters.
This data can then be applied to a basic rocket equation, where ϵ is the structural ratio of empty mass divided by fueled mass, and the payload ratio of upper stages/payload divided by total mass.
The resulting burnout delta-v is then reduced by the estimated aerodynamic losses and compared to delta-v range estimates.
This method allows to create a model about the concerned system, that provides the key data everyone is interested in: Whats the range and at which throw weight.
Quantifying the Trident II benchmark
Technical solutions applied in the Trident II, still represent state of the art in many ways, these include:
Carbon fiber filament casing
Carbon-carbon composite, single nozzles
High Isp fuel with increased density
Dense system design which reduces additional weight due to large interstages/shrouds
Flexseal flexible nozzle TVC system
Avoidance of thrust termination systems or retro-rockets
Aerospike to reduce impact of blunt and low length/diameter ratio aerodynamic design
Claims about range and throw weight are published for the Trident II as well as helping data points such as total weight.
Via the calculated model we can get a deeper understanding on what the key capability values and the performance of technical solutions are.
The major uncertainties with the Trident II comes first via its post boost vehicle (PBV), which weight is difficult to estimate. Second to that is the uncertainty about the effective Isp values of each of the three stages.
Results of estimated Trident II
The structural ratio for the applied technology is estimated at ~0,075 and can also be expressed as propellant mass fraction of 0,925. In comparison, accurate estimates for the well known late 1960's technology Minuteman III show a structural ratio of around 0,10.
Aerodynamic losses of total delta-v are estimated at 8% of the total delta V, where the slender, pointer and slower accelerating Minuteman III with its higher l/d ratio is estimated at around 6%
Isp of fuel and motor/nozzle combination is estimated conservatively at 263s sea level and 283 for the vacuum operating stages. Values of near 300s are rumored, but the applied values are still very high. This is due to the NEPE-like fuel utilized, whereas more conventional solid fuels have values of around 250s.
The large "footprint" PBV with the attached guidance section, and penetration aids is estimated at 1200kg. The total payload of the three stages excluding the PBV is set at 2800kg as reported in some sources.
Total weight is known to be 58,9t.
With these constrains the calculation model provides following results:
8000km range at 1600kg throw weight. This is well sufficient for the 14 x ~100kg Mk-4 re-entry vehicles full load, allowing for more or more sophisticated penetration aids. It is also in line with the claimed 8 Mk-5 RVs which are heavier and of higher yield.
13000km range at 800kg throw weight. This very long range ICBM configuration would have exactly half the throw weight, translating to 8 Mk-4 or 4 Mk-5.
Quantifying the DF-31 and DF-31A
In the previous post, the technical details of the DF-31 and DF-31A are described as far as possible with OSINT. There are no accurate drawings with dimensions, nor weights or throw weights available.
Compared to the Trident II benchmark, the differences are following:
Conventional aluminium based solid fuels
Less efficient 4-nozzle motor design for the DF-31 and DF-31A first stage
Less efficient TVC methods
High strength steel alloy casings (excluding the possibility of titanium alloy)
Lower aerodynamic losses for pointy DF-31 and higher for DF-31A
No need for a PBV as single warhead ICBM
Result of estimated baseline DF-31
The following dimensions and weights are assumed for the DF-31:
Total weight is estimated at ~40t
Diameter of stage I and II is estimated at 2,1mm
Diameter of stage III is estimated at 1,32m
Total length at 15,5m
Structural ratio of the three relative low l/d ratio stages is estimated at a combined mean value of ~0,13. Aerodynamic losses estimated at 6-7%. Isp is set at the reported, similar design, Minuteman value of 237s for the first stage and 255s for the upper stages. With these constrains the calculation model provides the following result: 7300km range at 500kg throw weight representing a single high yield RV. This is, with some uncertainty, validated by the supposedly leaked U.S intelligence report.
Results estimated for DF-31A
Dimensional changes of the DF-31A to the DF-31 include:
Shorter length of estimated 14,5m
Stage III diameter increased to 1,6mm
Weight increased to ~41t
Structural ratio of steel casing motor improved to 0,11-0,12, approaching Minutman III levels which uses titanium alloy in stage II and fiberglass composite in stage III. New TVC methods for upper stages of the DF-31A are also a contributor to this, as well as potential metallurgical improvements.
Aerodynamic losses are estimated at 7-8% Isp remains at 237s for stage I and significantly improves to 270s for the upper stages.
With these constrains the calculation model provides the following result:
10300km range at 500kg throw weight representing a single high yield RV.
The estimated and calculated values with their results, illustrate the impact of the different system parameters on ballistic missile performance.
At ~40t, the DF-31 is significantly lighter than the ~60t Trident. However better technology gives the Trident II a vastly superior system performance.
Of course the DF-31 may suit Chinas needs better in terms of costs and the employed counter-value nuclear warfare doctrine instead of counter-force.
It can also be used to interpret the need China felt to develop the DF-31AG, to attain 13000km-14000km range class performance and better penetration aids. DF-31AG may use a composite first stage or upper stages derived from the DF-41 development, the information is insufficient to do credible modelling.
The single largest contributer is shown to be the motor design: Its carbon composite, with flexible single nozzle TVC for the Trident II.
These features make the difference and the Trident II so high performing.