Deriving the Kinzhal Missile’s Actual Range and Speed: An Aerospace Engineering Analysis

7 min readAug 11, 2023

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An Open-Source Aerospace Engineering Analysis of the Kh47M2 Kinzhal Missile System indicates the missile’s public information is misleading the public.

Overview:

In this edition of The Engineer’s Perspective, I look at and derive the Range and Top speed of the Kinzhal, after noticing a discrepancy between its specifications and capabilities, in comparison to the missile that is said to have intercepted it — the Patriot PAC-3.

Problem Statement:

Some sources have made claims that the Kinzhal missile is basically an Iskander that has been adapted and integrated for use on aircraft.

However, a conflict appears to occur though when specifications of the Kinzhal are released on open media,, in that the Kinzhal’s reported range (Per BBC) is listed a 2000km approximate, as shown below:

While sources have listed the range of the Iskander as being approximately 500km:

Furthermore, according to Army Recognition, The Patriot PAC-3 Missile has a top speed of approximately Mach 5:

Open-Source Information of the Patriot PAC-3 Missile (Army Recognition)

Considering it is a Patriot PAC-3 missile that is said to have intercepted the missile, two questions have now come to mind:

If the Kinzhal is topping out at speeds around Mach 10, why is a Mach 5 missile intercepting it
If the Iskander and the Kinzhal missiles are essentially the same, then why is there such a significant discrepancy between the two missile’s estimated ranges?

Kinzhal Overview

Kinzhal Missile mounted on Mig-31 Foxhound

The KH-47M2 Kinzhal is an air-launched tactical ballistic missile that has been utilized most recently in the Russian Invation of Ukraine in 2022. It is believed that the Kinzhal is a derivative of the 9M723 Ballistic Missile, a mobile, ground launched, short range tactical ballistic missile often conflated with its launch platform’s name of Iskander (Hereafter, the 9M723 will be referred to as the Iskander Missile for simplicity’s sake and to acknowledge the name adoption from the media)

Iskander-M missile on the starboard erector arm of the 9P78–1 transporter erector launcher displayed at the «ARMY-2016» military-technical forum

Physical Analysis: Comparison between the Kinzhal and the Iskander Missile

One can compare the two missiles and see that the significant differences can be seen at the rear end of the missiles:

Highlighted in the red box, there is an extra Aero-Attachment to the Kinzhal that is absent in the Iskander missile (Illustrated below it). The Attachment is used to aerodynamically stabilize the missile and level it off as it is released by the M-31 during supersonic flight prior to the rocket motor activating and sending the missile downrange to its target as shown in the video below:

Analysis Methodology:

Part of the analysis methodology I will present to derive the speed and range of the Kinzhal will be:

Present open source intelligence (OSINT) gathering to get some basic specifications for both the Kinzhal and the Iskander missile, and from there,
Utilize basic kinematics to approximate a high-level, basic model of the Kinzhal and
Compare how the models align with the open source information in public.

Open Source Background Intelligence (OSINT):

CSIS reports The Kinzhal to have a reported range of 1,500–2,000 km while carrying a payload of 480 kg:

Graphic of open-source specs of the Kinzhal from the Center for Strategic and International Studies (CSIS)

A July 2018 TASS news report suggested the missile’s range would exceed 3,000 km if outfitted on the Tupolev Tu-22M3 bomber.7 It has similar dimensions as the OTK 9M723 Iskander-M; according to one report, the Kinzhal has a length of 8 m, a body diameter of 1 m, and a launch weight of approximately 4,300 kg.8

Open source information of the Iskander missile is shown below:

We can see that the 9K720 Iskander missile has an estimated operational range of 400–500km on CSIS and Wikipedia:

Open Source range estimations for the Iskander 9K720 missile (Wikipedia)

However, the masses of both missiles, as stated earlier are quite similar. It has not been explicitly stated that a new form of fuel has been utilized for the Kinzhal that allows it to attain essentially a 3.5–4x range increase over the Iskander though.

We will make the following assumptions for the model:

Missile attains a top speed (u) = Mach 6, converted to 2.07 km/s
Rationale:
I will assume a top speed of Mach 6 as after the burnout, the missile’s speed will drop to below Mach 5 prior to terminal terminal phase, which is where the Patriot PAC-3 is designed to intercept.
I also assume that the missiles use the same type of fuel.
Definition of Mach 1 = 767mph
Angle of launch is 45 degrees (To Maximize Range)
g = 9.80 meters a second
The missile’s starting altitude is at the top estimated altitude of two launch aircraft: The Mig-31 Foxhound and the TU-22M Bomber:
Mig-31 Foxhound:

Image of the Mig 31-Foxhound with a Kinzhal Missile (Military Watch Magazine)

Mig-31 Estimated service ceiling: 82,000ft, or approximately 25km
Mig-31 Estimated combat range: 1450km

Estimated combat range and service ceiling of the Mig-31 Foxhound (Wikipedia)

Tu-22M3 bomber:

Tu-22M Estimated service ceiling: 43,600ft, or approximately 13.3km
Tu-22M Estimated combat range: 2,500km
Illustrated Specifications of the Tu-22M below:

TLDR: Based on the open source information combined with the Kinematics equations used below, the Kinzhal, has the following specifications if it is an air-launched version of the Iskander 9K720 missile:

Top Speed: 2.07 km/s overall

Maximum Altitude: ~54km (Without starting altitude from Mig-31 and Tu-22M

Time Aloft: 297.5s

Maximum Range of:

478.6km when launched from a Mig-31; 1978.6 km when combined with Mig-31’s combat range
469.6km when launched from a Tu-22M; 2969.6 km when combined with Tu-22M’s combat range
The Actual Calculations:
I will assume that the performance characteristics of the Kinzhal to be similar to the Iskander, and will therefore use traditional Ballistic kinematics to estimate the behavior of the missile with the following equations:

Initial velocity assumed is approximately Mach 6, and converted to km/s is 2.07km/s:

2. Having Calculated the Velocity, we can derive the approximate distance the missile travels to 478.6 km when launched from a Mig-31 Foxhound, and 469.6 km when launched from a Tu-222M Bomber:

3. We can calculate the maximum altitude the missile achieves by:

Calculating the vertical velocity component
And bringing that into the hmax equation, and from there, derive that the missile achieves an altitude of approximately 54km independent of what altitude is is initially launched.

Review of the TLDR:

The Kinzhal, assuming it hits a low hypersonic speed of Mach 6, or 2.07 km/s, Travels approximately 478.6km and 469.6km when launched from the Mig-31 Foxhound and Tu-22M respectively.

The assumptions made for the model (Mach 6 speed, 45 degree launch), combined with the preliminary calculations, fit very well with the open source speculation that the Kinzhal is indeed an air-launched version of the Iskander missile.

Thus, the aforementioned Mig-31 launched distance estimate of 478.6 km, combined with the open source range of the Mig-31 Foxhound of 1,450km unrefueled (shown below) accounts for the 2000km range that is estimated for the Kinzhal

Open source information of Mig-31’s combat range (Wikipedia)

And likewise, the estimated distance of 469.6 km when launched from a Tu-22M accounts for the statements of an estimated range of 3000km when the missile is launched from a Tu-22M bomber:

Open source information of Tu-22M’s combat range (Wikipedia)

We can actually calculate how accurate the estimated calculation is vs the open source information:

The calculations and assumptions made for the model fit with a 96.4% and 98.98% accuracy then with the open-source assumptions about the system’s capabilities.