*A Technical Analysis of the Houthi Cruise Missile*

On September 14, 2019, the world’s largest crude oil processing facility at Abqaik, Saudi Arabia was struck by multiple airborne strikes that caused massive damage to key facilities known as oil stabilization plants, which make crude oil safely storable and transportable.

The reports and images from the scene pointed to severe damage that reportedly cut the oil processing output of the kingdom by no less than half—amounting to a loss of about five million barrels per day, about five percent of the world’s oil supply. As of Sept. 21, the consensus reported in the media is that the facility was attacked by 18 drones and seven cruise missiles, as reported by Fox.

The Yemeni Ansar Allah, aka Houthi rebel movement immediately claimed responsibility for the airstrike, but this claim is universally dismissed by so-called ‘experts’ and ‘analysts’ in the western media. The consensus argument is that the Houthi aerial weapons simply do not have the range to strike at that distance, about 1,200 km, or 750 miles.

Notably, no technical analysis of any kind has been published by qualified aeronautical professionals to support this assertion. For instance, the website *Arms Control Wonk*, which is widely cited in the media on various armaments issues, concluded that, it’s *‘unlikely’* the Quds-1 range would be *‘anywhere close’* to reach the struck KSA target from Yemeni territory.

It is necessary to point out that the author of this widely-cited ‘analysis’ lists no aeronautical engineering credentials, nor makes any attempt at a bona fide *quantitative* technical analysis. It is simply an *opinion* based on no scientific analysis whatsoever.

I am not aware of *any* published aeronautical analysis of the Quds-1 missile, which was first showcased by the Houthis last July.

The following technical analysis will establish, based on accepted principles of physics and aeronautics, that the Quds-1 is indeed capable of a flight range in excess of 1,200 km—capable to hit Abqaik from Houthi territory.

**The Benchmark: **

*Raytheon ‘Tomahawk’ Land Attack Missile*

In this analysis, we will proceed to rely on the known characteristics of the Tomahawk, such as its physical dimensions, engine thrust and fuel consumption in cruise, in order to determine the same parameters for the Quds-1.

We will compute the key aeronautical parameter for the Tomahawk, its aerodynamic drag, relying on engine manufacturer information for its cruise thrust and fuel consumption.

The basic physical principle is that thrust must equal drag in straight and level, unaccelerated flight, as per the action-reaction principle.

Thus, knowing the engine thrust of the missile in cruise, we also know its drag.

The published engine data for the Tomahawk engine includes cruise thrust and fuel consumption. It means the analysis can accurately determine the drag of the T-Hawk.

We will do the same for the Quds-1, which uses a Czech-built turbojet engine whose technical characteristics and specifications are readily available from the manufacturer.

Looking at the Tomahawk we note that it has a cylindrical fuselage supported by fairly small wings, as well as a cruciform tail section with movable surfaces for flight maneuvering. It is readily apparent that such a sleek and streamlined shape will generate minimal drag, or air resistance.

The main source of drag for such a flight vehicle will be the cross-sectional area of its fuselage—think of a wide-body passenger jet, which will have greater drag than a narrow body airliner. This is called form drag. In addition, skin friction drag is also obviously dependent on the size of the flight vehicle and its wetted surface area. Form drag and skin friction drag together constitute the entire parasitic drag of a flight vehicle.

Cruise missiles are designed to fly fairly low to the ground or sea in order to avoid detection by enemy air defense radar. At these low altitudes the air is dense, and the missile is designed to fly at high speeds; this means that a small wing will produce enough lift to keep the craft aloft.

By contrast, a passenger jet flying at high altitudes in thin air requires a much bigger wing to support its weight.

Since the two cruise missiles under comparison have the same basic layout, their respective aerodynamic drag will be linearly proportional to their respective fuselage cross-section areas—which in turn are a function of fuselage diameter.

Tomahawk Dimensions:

Diameter: 20.4 inches [0.52 m]

Length: 18 ft, 3 in [5.56 m]

Wingspan: 8 ft, 9 in [2.67 m]

**Quds-1 Dimensions **

The Houthis have not released any dimensions or specifications for the Quds-1 cruise missile. However, it is possible to accurately estimate key dimensions from published photos, by scaling to the known dimensions of the Quds-1 engine, which is the TJ-100 turbojet, manufactured by PBS Aerospace in Czechia.

The Saudis reportedly recovered wreckage in June, 2019 of a TJ-100 engine, following a Houthi airstrike that month on the Abha airport, and displayed photos of the engine to the media. The missile in that particular attack was not the Quds-1, but another Houthi cruise missile type, called the Ya Ali. It does confirm however, that the Houthis have access to the TJ-100 engine.

Four days after the Abqaik attack the Saudis displayed wreckage of cruise missile pieces that show what appears to be two TJ-100 engines, as well as airframe pieces, including a nearly intact empennage that bears a strong similarity to Quds-1:

Just by looking at the Quds-1 engine from photos released by the Houthis, and comparing to the TJ-100 we see that it is almost certainly the same engine, or a copy thereof.

We see from the above comparison pictures that the only difference is a slightly longer engine inlet nacelle on the Quds, compared to the Subsonex aircraft. This is due to the fact that the missile flies at a much higher speed than the small piloted airplane—about double. This requires a more gradual diffusion in the engine inlet, whose purpose is to recover as much ram pressure as possible.

Scaling from the known TJ-100 engine diameter of 10.7 inches [0.27 m], it’s possible to give a good estimate of the crucial Quds-1 fuselage diameter, which, in turn, will let us compute its drag, by direct comparison to that of the Tomahawk.

In this photo from the *Arms Control Wonk* website, we see the scaling measurements performed on the photo, resulting in a fuselage diameter of approximately 13.4 inches [0.34 m]. This scaling measurement appears accurate.

**Computing Cruise Missile Drag**

The Tomahawk cruise missile is powered by a small turbofan engine from Williams International, the F107.

The manufacturer data sheet for this engine is available here:

The static thrust of this engine is 635 lbf [pounds of force], a little over twice the rated static thrust of the current TJ-100, at 292 lbf. However, we will assume the use of the earlier version TJ-100A, which was rated at 247 lbf of static thrust.

It is important to note that we are concerned with the engine thrust at the missile’s operational cruise speed and altitude, which values are highlighted in the table—not the static thrust, which is of no use in computing aerodynamic drag [since there is none when standing still.]

Using this information, we can compute the Tomahawk’s total flight drag, which must be equal to the engine thrust, in straight and level, unaccelerated cruise flight.

We note that the F107 engine thrust is 318 lbf at an altitude of sea level [SL; 0 ft] and standard day conditions, at a flight speed of Mach 0.7, which is 463 knots or 533 mph.

That means the Tomahawk’s total drag must also equal exactly 318 lbf, since the two opposing forces must be in equilibrium.

We now need to find the air resistance at this speed and altitude, which is called dynamic pressure. This is the force you feel when you stick your hand out the window while driving on the highway. Dynamic pressure is the product of air density and velocity squared, divided by two.

Standard day air density is 1.225 kg/m^3, the flight speed of 533 mph is 238 m/s [meters per second], so the dynamic pressure works out to ~35 kPa, which is 726 lbf/ft^2. [A good atmospheric calculator here.]

Now that we know that one square foot of flat surface area, pushing through the air at 533 mph and oriented with its flat side perpendicular to its direction of flight, has an air resistance of 726 lbf, we can compute the Tomahawk’s actual drag area by dividing our engine thrust of 318 lbf, by the dynamic pressure. We get a drag area of 318/726 = 0.44 square feet.

**Computing the Quds-1 Drag**

Since the drag of the two missiles is largely a function of their respective cross-sectional areas, we compute the Quds-1 drag by scaling to the now known drag area of the T-Hawk of 0.44 ft^2.

The Tomahawk with a diameter of 20.4 inches has a cross-section area of 2.3 sq ft. The 13.4-inch diameter Quds has a cross section area of 0.98 ft^2—just 43 percent of the area of the larger T-Hawk [area is a function of the *square* of diameter].

It’s like comparing a Boeing 737 to the wide-body triple seven; the larger airplane will obviously have more drag, and will therefore need more powerful engines that produce more thrust, and burn more fuel.

We note that the Quds has its engine mounted on top of the fuselage, which will add a little extra drag, compared to the T-hawk’s fuselage-buried engine, with just a small air inlet scoop underneath. [Although the underslung air scoop will be less efficient in terms of ram pressure recovery and will reduce engine performance in comparison to a conventional inlet nacelle that gives a straight path to the engine compressor.]

To compensate for this extra drag, let’s assume that the Quds has 50 percent of the drag of the T-Hawk instead of 43 percent. This means it would need half the thrust to match the T-Hawk’s performance of 533 mph.

However, it is not necessary for the Quds to fly at over 500 mph. The TJ-100A engine is approved for speed up to Mach 0.8, but if we assume a speed of 425 knots true airspeed [M0.64; 489 mph], which is still very fast, the Quds will face lower air resistance, due to the lower dynamic pressure. We note from the math for dynamic pressure that it is a function of velocity squared, so lowering the speed will lower the air resistance quadratically.

Working out the numbers we find that the dynamic pressure at 489 mph [M0.64; 425 knots], sea level, standard day is just 612 lbf/ft^2 [pounds force per square foot], more than 100 lbf/ft^2 less the T-Hawk’s air resistance of 726 lbf/ft^2, flying at 533 mph under the same conditions.

With the Quds drag area being not more than half of the T-Hawk, this equates to a Quds-1 drag area of just 0.22 sq ft; total drag force is then 0.22 ft^2 * 612 lbf/ft^2 = 135 lbf. Since thrust must equal drag, it means that only 135 lbf of thrust is required from the TJ-100 engine for this missile to fly at 489 mph, at sea level standard day conditions.

We see that the smaller fuselage of the Quds, plus a flight speed just 44 mph slower results in thrust required of less than half of that of the T-Hawk.

**TJ-100 Fuel Consumption**

The TJ-100A specific fuel consumption [SFC] is given by the manufacturer as 0.111 kilograms of fuel, per newton of thrust per hour, which is 1.09 pounds of fuel per pound of thrust per hour [lbm/lbf/hr].

However, this figure is at the static condition, which means the aircraft is standing still. As forward speed increases in any aircraft, the thrust decreases, due to the fact that the speed of the aircraft is subtracted from the speed of the jet flow exiting the engine, which remains about the same.

The thrust force of a jet engine is the air mass flow through the engine, times the speed of that gas flow as it exits the engine jet nozzle. The Thrust Equation tells us that as the speed of the aircraft increases, the thrust must decrease.

What this means for fuel consumption is that less thrust is being generated in flight, for the same amount of fuel burn; as the aircraft flies faster thrust continues to decline. This holds true for any aircraft, due to basic physical principles.

We note in the performance Chart from Williams that the T-Hawk engine has a 52 percent higher specific fuel consumption in cruise than it does at maximum power static [1.043 lbm/lbf/hr / 0.683 lbm/lbf/hr = 1.52].

Does that mean the TJ-100 will also see about a 50 percent increase in SFC in cruise flight? The rule of thumb answer is *‘yes,’* but we will verify this by performing a mathematical computation known as a thermodynamic cycle analysis, which is used in jet engine design to determine the optimal general characteristics of the engine, such as mass flow, compressor pressure ratio, thrust, and fuel consumption, both in static condition, but especially at the design point flight airspeed and altitude.

In this case, we will be using the cycle analysis method to first determine some key unknown characteristics of the engine at its static condition, such the compressor pressure ratio, and the combustion chamber temperature.

We know from the above chart the engine’s static thrust of 1100 newton [N], its specific fuel consumption at maximum static power of 0.111 kg/N/hr [1.09 lbm/lbf/hr], and the turbine outlet temperature of 730 C. The below chart gives the air mass flow of the engine as 1.85 kg/s [4.08 lbm/s]. This is sufficient data to accurately compute the engine fuel consumption in flight, at various airspeeds.

The information from the above and below charts is from the TJ-100 manufacturer’s published data, available here.

The results of the cycle analysis provide the following engine parameters at the static condition:

We see that our cycle analysis matches the manufacturer’s published engine specifications very closely, to within rounding error for three significant digits. The highlighted parameters are an exact, or almost exact match to the above TJ-100A charts.

Having found the key unknown engine parameters of compressor pressure ratio, combustion temperature and the component efficiencies of the compressor, turbine, nozzle and combustor, we can now proceed to compute the engine’s performance parameters at cruise condition.

The cruise condition corresponds to an ISA standard atmosphere and 0 ft altitude; two cruise cycle analyses have been computed: one corresponding to the manufacturer chart for 91 percent of rotor speed [N] and another at reduced cruise power engine speed of 84 percent of N.

These two cruise speeds correspond to the below flight speeds of the Quds-1.

The two cruise cycle analysis parameters are as follows:

Again, we note that the key parameters of turbine outlet temperature [highlighted in green] exactly match the manufacturer data.

Now let us compute how much fuel is required to fly a 1,200 km mission [746 statute miles]:

We note that the maximum drag area for both flight speeds matches the computed drag area for the Quds missile.

We now also know the total fuel consumption for a 1,200 km flight—based on the flight speed times the flight duration needed to cover that distance. The only question that remains is whether the Quds-1 is capable of carrying enough fuel.

**The
Quds-1 Fuel Capacity**

Knowing the diameter of the Quds-1 fuselage, it is necessary to ascertain the position and length of the fuel tank. In any aircraft, the position of the fuel tank[s] is centered in close proximity to the aircraft’s center of gravity, in order to maintain the craft’s crucial balance in flight, as fuel burns off and weight is shed from the aircraft in flight.

Since the amount of fuel carried by aircraft is a significant proportion of total weight [typically between one quarter and one half for most jet aircraft] the placement of the fuel tanks to maintain balance is vital. In passenger jets and combat aircraft the fuel is usually located in tanks within the wings, as well as the fuselage center section where the wing is attached.

In a cruise missile the wings cannot carry fuel due to their small and thin dimensions; the fuel tank must always be located in the cylindrical fuselage and centered very close to the center of gravity, which, in turn, will be located just ahead of the wing center of lift which is located at about the one quarter-chord point of the wing.

[The CG must be ahead of the center of lift, or neutral
point, for positive aircraft pitch stability. Aerodynamically, a cruise
missile is actually more of an aircraft than a *‘missile.’*]

This marked up image of the Quds-1 shows the location of the fuel tank section.

Again, we scale from the known length of the TJ-100 engine which is about 2 ft [not including the inlet nacelle.] We see that the fuel tank section is *at least* 6.5 ft in length.

This dimension allows us to easily compute the internal fuel tank volume, which works out to about 6.4 cubic feet [180 liters; 48 US gallons]. The weight of aviation kerosene on which turbine aircraft run is somewhat variable within a narrow range, but the ‘standard’ weight’ used by pilots for computing aircraft weight and balance before each flight is 6.7 lbm per gallon.

This gives the Quds-1 a total fuel capacity of about 320 lbm. As computed in the above tables for range, the Quds-1 is able to fly 1,200 km with a total fuel load of between 276 lbm and 310 lbm.

It should be noted that flying at even slower speeds than the two flight speeds computed here will result in even greater range. With 300 pounds of fuel, this missile with this engine should be able to fly 1,400 km or more, flying at a speed of about 375 mph [325 knots; Mach 0.5]. At this speed, dynamic pressure is only 358 lbf/ft^2 and requires only 79 pounds of engine thrust.

That is TWICE the ‘estimated’ range of 700 km widely cited in the media and attributed to ‘experts.’ No actual expert in aerodynamics and jet propulsion could possibly arrive at such a ridiculous figure. It would require an engine fuel consumption of DOUBLE that of the actual TJ-100 engine.

**Let’s Get ***Technical* About Jet Engines

*Technical*About Jet Engines

The layman reading this article may be wondering just how this concept of *jet engine cycle analysis* really works. It is not difficult to understand if we understand some fundamental mechanical facts about gas turbine engines. Let’s start with a cutaway illustration of a typical turbojet engine.

We see that the turbojet engine is really a fairly simple device. There is actually only one moving part, the rotating assembly that includes the compressor in front, the turbine in back, with both attached to a common shaft. The entire assembly rotates at the same speed.

The functionality is simple: air enters the inlet and is compressed by the rotating compressor blades. The compressed air flows continuously from the inlet, through the compressor and through the combustion chamber, where fuel is added and burned, increasing the air temperature [which is now a gas composed of both fuel and air molecules.]

The flow continues steadily, without interruption, throughout the engine, from the combustor to the turbine, which is made to rotate by the hot gas flowing through its blades—in the same way a windmill or wind turbine is driven by air flowing through its blades.

The turbine, being connected by the engine shaft to the
compressor, provides the *work* required to turn the compressor and compress
the air before it enters the combustor.

After flowing through the turbine, the hot gases have lost some of their pressure and heat energy in driving the turbine—but there is still plenty of energy left to be squeezed through a jet nozzle that works in the same way as a simple water nozzle in your yard. The pressure energy in the gas [which was imparted by the compressor and only partially depleted in the turbine] is converted to kinetic energy, or speed energy, by being forced through a smaller opening.

The result is a very fast-moving stream of gas exiting the back of the engine, which, in turn, causes an equal force in the opposite [forward] direction, as per the physical reality of *action-reaction.*

This force is thrust, and it is strictly a function of the mass flow going out that jet nozzle, and the speed of the mass flow.

It’s important to pause here and point out a couple of important physical principles. The first is that the flow of air into the engine and out the nozzle is constant and without interruptions.

This means that the amount going in must equal the amount coming out, as per the conservation of mass principle. There is however, the added mass of the fuel to consider, so the jet exhaust mass flow is actually slightly in excess of the air intake mass flow of the engine [although this added mass is relatively small, since air to fuel ratios in jet engines are typically over 50 to 1].

Another important consideration is the physical fact that only *pressure energy* can be converted to work energy in *any* heat engine—this includes everything from a jet, to a car engine, to the refrigeration engine in your air conditioner.

That is why every heat engine must have a means of
compressing its working fluid. In jets, cars and any other *air-breathing*
engine, the working fluid is air—this is what must be compressed in order to have
a working engine.

The heat added in combustion by itself cannot do any work if there is no compression, but it does allow the pressure energy to do MORE work, since we have also added heat energy—thus the total energy of our fluid stream is increased greatly.

Think of a balloon. If you inflate it, you have expended work energy to blow air into it. Once inflated it contains pressure energy that is capable of doing work. When you let go of the balloon lip, it performs work by exhausting a stream of air that propels the balloon around the room—physically a process identical to a jet engine.

If you were to use *hot* air to blow up that balloon [and if the balloon material could withstand the temperature], the amount of work released will be greater—and the balloon will jet around the room more energetically.

**Understanding
the Turbojet Cycle**

In the above diagram more detailed information is presented about what physically happens in each stage of the turbojet engine. [From Cengel; *Thermodynamics: An Engineering Approach;* 8’th Edition]

We note that the engine is divided into six ‘stations’ and the corresponding temperature-entropy graph on the left shows what happens along the way, as the airflow makes its way through the engine.

We note further that station 1 corresponds to the air just ahead of the engine, before it has even entered. If we imagine that jet engine moving through the air at a high speed we realize that as the air enters the engine and goes from point 1 to 2, it will be rammed into the engine, resulting in a compression of the air, as well as an increase in its density and temperature.

The chart on the left shows that at station 2, the
compressor face, temperature has already increased from the ambient air at
station 1—indicating the ram compression that has taken place. If we now refer
to our above tables of the cycle analysis for the TJ-100A engine in cruise
flight, we now can make sense of the parameters: *Inlet pressure ratio;
compressor face temperature; total density; and dynamic pressure.*

All of those values have *increased* from the condition
of the ambient air at station 1—all due to the speed of the engine hitting that
stationary air and packing it into its inlet due to the ram effect.

So before the air has even entered the compressor, we already have some compression taking place!

We also note from the above cycle analysis tables that the mass flow of air is higher at the high-speed condition than it is at static: 1.98 kg/s at M 0.64, versus 1.85 kg/s at static. [In the slower flight condition at M 0.55 the airflow has decreased a little from static due to the fact that the engine rotational speed has been reduced substantially; the compressor simply cannot ingest a high airflow when it is rotating more slowly].

As the air moves through the compressor, we see a
significant temperature rise in the graph. This is due to the fact that
compressing air always raises its temperature. Now we refer back to the tables
and the parameter *compressor outlet temperature,* which is station 3 on
the engine.

The flow through the combustion chamber is from station 3 to 4. We see on the graph that heat is added [q in]. Thus our cycle analysis has computed a combustion temperature for each of the two flight speeds examined. This is a crucial aspect of the engine performance, since the amount of heat added in the combustion chamber is strictly a function of the amount of fuel burned.

Since the whole point of our cycle analysis has been to compute the fuel consumption of the engine in flight, this parameter is key.

Another important point is that there is no increase in pressure in the combustion chamber, despite the addition of heat. This is fundamentally different from a car engine with which most people are familiar, where the combustion of the fuel greatly increases the pressure in the cylinder.

The difference is that a car engine cycle is a stop and go process, with four distinct piston strokes, unlike the jet engine where the flow is constant and the engine is open at both ends at all times. The car engine cylinder closes its valves when the spark is ignited and combustion occurs, greatly increasing the pressure in the cylinder.

It is this closed volume that is absent from the jet engine, and hence the pressure throughout the combustion chamber remains the same, as seen in the graph on the left [P = constant].

The combustion that happens in the jet engine burner *does* result in an acceleration of the gas flow, due to the heat, but since the back of the engine is open there is no physical means by which the pressure can increase. In fact, the pressure in the gas turbine combustor will always *decrease *by a small amount, due to the inevitable physical losses in this process.

This is why our cycle analysis table has the parameter ‘pressure recovery,’ which in this case is 0.95, or 95 percent—meaning the gas flow has lost five percent of its pressure on its way from the compressor through the burner.

Also worth noting here is that once the gas turbine engine combustor has been ignited, the flame burns continuously—just like your house furnace. A spark is only needed to start the engine.

We note on the graph that the engine temperature reaches its peak at the combustion chamber. From there the flow enters the turbine at station 4 and we see the temperature going down as work energy [both heat and pressure] is extracted by the turbine.

At the turbine exit point, station 5, the gas flow has lost about half of its temperature, as we see in the graph—the remaining pressure and heat energy is expended in the nozzle, which does the work of accelerating the jet flow to a very high speed. We note from our cycle analysis tables that this exhaust jet speed for the TJ-100A at static condition is nearly 600 meters per second, which is over 1,300 mph!

That’s an impressive blast from an engine weighing less than 50 pounds.

So that is the thermodynamic cycle of the turbojet engine explained. We can see that, knowing the basic engine parameters provided by the manufacturer [static condition], it is a straightforward method to compute the key unknown parameters [like combustion temperature and the various efficiencies at the six engine stations].

Once we have computed the unknown parameters with a close match to the key published data points like thrust, specific fuel consumption, mass flow and turbine outlet temperature, we then proceed to take that static condition baseline and compute the same parameters [plus a few more] for the engine in flight.

Now looking at the parameters for the engine at its two respective flight speeds, a question may arise as to why the compressor pressure ratio has decreased, as compared to static.

The first reason is that in cruise, the engine is running at a slower rotational speed, N. The compressor’s performance is based on how fast it is spinning—the faster it spins, the higher the compression. If you slow down the engine rpm, the compressor will not compress as much.

A second and important reason also comes into play, and that is the temperature of the air entering the compressor. We have noted already that at high flight speeds, the air is compressed in the engine inlet and its temperature has increased from ambient to station 2 on the compressor face.

The basic physical principle at work here is that hotter air requires *more work* to compress. The opposite is true of colder air. In jet engine design, this can be precisely calculated by means of something called the *corrected shaft speed.*

This means that if the air entering the compressor is hotter, the compressor will perform as if it is spinning at a slower speed. [The opposite is true of colder air, which is why jet engines get much more efficient as they climb to the high flight levels where the air temperatures are usually about 50 degrees below zero.]

In the case of a cruise missile flying low, the air entering the compressor is quite high at these high flight speeds. Our tables show a compressor face air temperature of close to 40 C [from a starting point of ambient temperature of 15 C; if the actual ambient temperature is higher than this standard ISA temperature, then the compressor face temperature will be higher still.]

Combined with the reduced engine speed to begin with, plus the even lower *effective *engine rpm due to the hot air at low altitude, the result is a drop in compressor pressure output.

However, we recall that at these high speeds the ram pressure is already substantial [about 1.3 pressure ratio in the case of the M 0.64 flight speed], so the overall pressure ratio [OPR] is the compressor pressure ratio multiplied by the ram pressure ratio, which equals 4.9. At the slower flight speed we see OPR of only 4.2.

This is a good time to note that a gas turbine engine’s efficiency is determined in large part by its pressure ratio—the latest large turbofans used on passenger jets have OPR of 50 or even higher.

Thus we see that in flight, the exhaust gas velocity also goes down, as the OPR declines. This is directly related to the lower pressure—we recall that only pressure energy can be converted to work energy in a heat engine…remember the balloon, blow it up harder and it will zoom around a lot more energetically.

**Component
Efficiencies: The Final Piece of the Puzzle**

We have to this point explained many of the parameters of the turbojet cycle and how they may be analyzed. But a number of the parameters, such as compressor and turbine efficiency, and pressure recovery in the inlet, combustor and nozzle have not.

The above graph shows what is called an *ideal* engine cycle, where each of those components is operating at 100 percent efficiency, with zero losses. This is not true in the physical world.

In this graph we see the effect of what are called *irreversibilities* in the Brayton cycle on which all jet engines, and gas turbine engines, generally, operate.

The horizontal line represents entropy, which are losses in efficiency, and we see that from point 1, which is the compressor in this generic gas turbine representation, the dotted line veers to the right, meaning that some work energy in the compressor is wasted. This wasted energy manifests itself as heat, which is why the point 2a, which is the end of the compression stage, is higher on the temperature scale [a stands for ‘actual’].

After the compressor, the line from point 2 to 3 is the combustor, and we see a loss of pressure in the combustor, as mentioned previously.

The turbine work from point 3 to 4 also veers to the right,
and the ending temperature of the turbine stage is higher than ideal [s stands
for *isentropic*, or lossless]. This means that not all of the heat energy
has been utilized for useful work—some is left behind and goes out the exhaust
pipe unutilized.

We also see that there is a pressure loss during the heat rejection, where the cycle goes from its ending point at the exhaust [4a], to its beginning point back at 1, the compressor inlet.

In our cycle analysis this pressure drop in the exhaust
nozzle is given as the parameter *‘nozzle pressure recovery.’*

The total work of the engine is represented by the area bounded by the lines, so we see how the irreversible losses shrink the area on the graph and decrease the efficiency of the machine.

The various component efficiencies computed in the above cycle analysis for the TJ-100 represent fairly typical values for a small turbine engine: compressor and turbine efficiencies on the order of about 80 percent, and inlet, combustor and nozzle efficiencies on the order of the mid-90 percent range.

**A closer look at the TJ-100 Engine**

In the manufacturer’s data sheet, the engine is described:

TJ 100 is single-shaft engine with single-stage radial compressor, annular combustion chamber, single-stage axial turbine, and stationary exhaust jet.

A single-stage radial compressor, also known as a centrifugal compressor is basically a turbocharger impeller.

These centrifugal compressors are widely used in small gas turbine engines, including small aircraft engines—turbojets and turbofans for light executive jets; turboprops for utility aircraft and turboshafts for helicopters.

In reference to the illustrations of the turbojet engine above, the axial-flow compressor with multiple compressor wheels is replaced with a single centrifugal wheel.

As regards the turbine, we note that there is only a single turbine wheel of the axial flow variety, rather than the multiple stages shown in the above illustrations. The reason is that with its single compressor and relatively low pressure ratio, there is no need for a second turbine stage.

The entire rotating assembly of the TJ100 will look something like this:

The gear in the middle of the shaft would be used to drive the engine fuel and oil pumps and a generator. [This rotating assembly appears to use a radial-flow turbine wheel, as used on turbochargers].

Basically the TJ-100 engine is not much more than a turbocharger core with a burner and a jet nozzle. Here is a turbocharger rotating assembly, inside its center housing:

Here is a compressor map for a large performance turbocharger for car engines.

We note that at a pressure ratio of 4, it has an adiabatic efficiency of 77 percent, and flows 200 lbm/min, which is 1.5 kg/s—not much less than the compressor on the TJ-100. In fact there are bigger turbos with higher pressure ratios and mass flows than the TJ-100.

So we see that the TJ-100 is a very simple and basic design, that weighs only about 50 lbm. The small Williams turbofan used on the Tomahawk weighs nearly three times as much, for a thrust output that is only a little more than double.

**The
Turbofan Engine**

Here we see the inner workings of the turbofan engine. We notice it has two rotating assemblies, one for the fan, driven by its own turbine at the very aft end, and one for the *‘gas generator’* or engine *‘core’* which is basically the same as the turbojet engine.

The two assemblies, called spools, rotate *independently *of each other, with the fan spool shaft passing concentrically through the larger core shaft.

Naturally, this type of engine is a lot more complex mechanically. With very large fans and high bypass ratios that we see on modern passenger jet turbofans, the fan turbine stage may have as many as five turbine wheels.

Here is a cutaway of a small turbofan used on Russian cruise missiles.

We see that the flow splits off into two separate passages just aft of the fan, with the core flow going into first a small, single radial flow compressor wheel and then into a centrifugal impeller like we see on turbos and small gas turbines like the TJ-100.

At the turbine section, we see one turbine wheel for each of the two spools, with the concentric shafting clearly visible.

This is a low-bypass ratio engine—we can see clearly that the ratio of the bypass opening is about the same size as the core duct, implying a 1 to 1 bypass ratio [as on the Williams F107].

The advantage of the turbofan is that it moves a greater mass of air—the cold stream from the bypass duct, and the hot stream from the core. This means more thrust since thrust is the product of mass flow and exhaust velocity.

At subsonic speeds turbofans have an additional advantage in propulsive efficiency, since it is more efficient to move a greater mass of air, at a slower exhaust speed, than a smaller mass at higher exhaust speed like the turbojet.

However, at supersonic speeds the turbojet regains the advantage. The Concorde used Olympus turbojet engines to cruise without reheat [afterburner] at Mach 2. It had better fuel efficiency than the Tupolev Tu-144 which used turbofans—but later switched to the Kolesov turbojet engines when those were developed, and saw a substantial increase in fuel efficiency and range with the turbojets.

It’s worth noting that the new generation Russian Kalibr cruise missiles use turbojet engines, not turbofans, and they have range matching or exceeding that of the T-Hawk.

In looking at our cycle analysis it is clear that the TJ-100 engine is not optimal for a high-subsonic cruise missile flying low. A turbojet for this flight condition would be more efficient with a higher pressure ratio, perhaps six or seven—which is doable with a single centrifugal compressor.

That would bring the exhaust gas velocities to a higher speed in flight at Mach numbers over 0.5. Engine fuel efficiency would increase with the higher pressure ratio.

**However, the TJ-100 is capable of doing the job as our cycle analysis indicates. **

A maximum range of 1,400 km is entirely possible with the Quds-1 missile. It should be noted that the range numbers attained in this analysis could in fact be *higher *if the Quds were to fly some portion of its en route flight at a higher altitude—even at 1,000 ft the numbers would be better.

There is no doubt whatsoever, that the Quds-1 powered by the TJ-100 engine is indeed capable of hitting the Saudi oil facilities at Abqaik. The *‘experts’* who claim otherwise are actually nothing of the kind.

Fascinating article… you can’t always believe what you are told by the media! Does the weight of the “missile” affect its fuel consumption (the navigation equipment and warhead)? Does the Quds-1 carry an equivalent warhead? I’ll go back and reread the article when i have more time, thanks for the thorough research.

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Pol, thanks for your interest…there are no published data on the weight of the Quds-1…the weight of the Quds-1 would scale approximately in the same as we have used to scale the drag…these scaling laws are well known in physics…for instance we used the measured [from imagery] fuselage diameter to to scale to the known Tomahawk drag…this is valid because both flight vehicles have the same configuration and planform…if you look at passenger jets you see that this holds quite precisely…for instance a Boeing Triple Seven has a fuselage diameter roughly twice that of a 737, which means four times larger cross section area…if you compare engine thrust in cruise [they both cruise at about the same speed, roughly Mach 0.8], you find that indeed the engine thrust of the larger plane is about four times that of the narrow body…and since thrust must equal drag in straight and level, unaccelerated flight, it means the drag has scaled completely linearly from fuselage cross section area, as we have done here…this is a well established scaling rule in aeronautics…if we were to actually measure the entire wetted surface area of both planes, we would find a similar relationship…Mass [or weight] scales in a similar way, and we could make an estimate for that, but it is not necessary…and mass does not affect fuel consumption in a major way…aerodynamic drag is the main force that the engine thrust has to overcome…weight is balanced by the lift created by the wings…if we were to estimate the wingspan and wing area from the photos, we would likely find that it has likewise scaled [in comparison to the T-Hawk] in the same way as the fuselage cross section area…

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Great analysis. What would be the effect of lowered weight at the terminal phase when tanks are near empty. Can we expect a significantly higher terminal speed than the average cruise speed? The engine can also be run at highest power at terminal phase too for the short period of time.

The Qods-1 also benefits from it’s fixed wings which don’t occupy tank space.

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The lower weight in the terminal stage due to fuel burnoff could result in a little more speed due to reduced drag that comes with lower weight [more weight means more lift is required by the wings, which brings with it lift-induced drag]…but the increment would not be ‘significant’…upwards of 400 mph is pretty fast anyway, especially down low in the atmosphere…the reason is that increasing speed in any aircraft means the power required increases approximately by the cube, not linearly…for instance, in order to double speed, say from 200 mph to 400 mph is going to require 2^3 times more engine power, that’s eight times more power, or 2^2 [four times more thrust]…this is a topic of basic flight physics that I will explore in future installments…

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