Nomenclature

I

radiation intensity (W/sr)

L

path-length (cm)

M

mach number (-)

P

pressure (Pa)

T

temperature (K)

e

infrared emission flux (W/m²)

$\varepsilon$

emissivity (-)

k

absorption coefficient (cm⁻¹)

m

mass flow rate (kg/s)

n

molar fraction (-)

τ

transmissivity (-)

λ

wavelength (µm)

i

intensity flux (W/m²-sr)

r

recovery factor (-)

Subscripts

a

air

ac

aircraft

acs

aircraft surface

b

blackbody

bg

background

bot

bottom

cont

contrast

earth

earthshine

f

fuel

int

internal

p

plume

s

surface

sky

sky-shine

w

wall

∞

free stream

s9

static nozzle exit

Abbreviations

CD

convergent divergent

EM

electromagnetic

IR

infrared

LWIR

long wave IR (8–12 μm) band

LBL

line by line

LOWTRAN

low resolution atmospheric transmission

MANPADS

man portable air défense system

MOEA

multi-objective evolutionary algorithm

MSNBCK

multi-scale narrow band correlated-K

MWIR

medium wave IR (3–5 μm) band

SWIR

short wave IR (2–3 μm) band

SAM

surface to air missile

2.0 IR signature of aircraft bottom surfaces

The IR signature (IR contrast) of the aircraft in a wavelength band (λ₁−λ₂) is given by I _cont = I _ac − I _bg . Where I _ac is the IR intensity of the aircraft which includes the internal emission, and the reflected radiation. I _bg is the radiation of the background replaced by the aircraft. When the aircraft is seen from the bottom, the background will be sky. The IR radiation flux from the bottom surface of the aircraft will be:

(1) \begin{align} {i_{s - cont}} = {i_{s - bot}} - {i_{sky}}\!\left( {{\rm{W/}}{{\rm{m}}^{\rm{2}}}{\rm{ - sr}}} \right) \end{align}

The i _s-bot consists of IR (internal) due to the surface temperature of the bottom surfaces and the reflected skyshine, sunshine and earthshine. Normally the sky reflection from the aircraft is very low and can be neglected. The earthshine (earth radiation reflection from the aircraft) is mostly important from the bottom view of the aircraft and is significant for the low-flying aircraft [Reference Mahulikar, Potnuru and Rao30]. The sunshine (reflection of sun radiation from the a/c) is significant in the SWIR band followed by the MWIR band and negligible in LWIR band. In the present study, it assumed that aircraft is flying in the night sky, thus sunshine emission is neglected. The IR intensity flux, which is defined as radiation energy emitted in a given direction, per unit normal area, and per unit solid angle leaving the aircraft’s bottom surface can be given by:

(2) \begin{align}{i_{s - bot}} = {i_{s - bot - int}} + {i_{s - bot - earth}} \end{align}

The i _s-bot-int is the intensity flux due to the surface temperature of aircraft bottom surfaces, given by i _s-bot-int = ɛ _acs e _s-bot-int /π, where ɛ _acs is the emissivity of the aircraft bottom surface and e _s-bot-int is the blackbody emission of the aircraft bottom surface in the wavelength band λ₁−λ₂. The black body emission (e _s-bot-int ) at T _w wall surface temperature is given by:

(3) \begin{align}{{\rm{e}}_{s - bot - int\left( {\lambda1 - \lambda2} \right)}}\left( {{T_w}} \right) = \mathop \int \nolimits_{{{\rm{\lambda }}_1}}^{{\rm{\lambda }}2} \frac{{{{\rm{C}}_1}}}{{{{\rm{\lambda }}^5}\left( {\exp \!\left( {\frac{{{{\rm{C}}_2}}}{{{\rm{\lambda T}}}}} \right) - 1} \right)}} \end{align}

Where C₁= 0.596×10⁻¹⁶W-m² and C₂ = 0.014387m-K. The aircraft bottom surface temperature depends on the flight altitude and Mach number. The maximum temperature that the bottom surface can attain for subsonic to supersonic Mach number range is the recovery temperature (T _r ). In the present study the bottom surface temperature is assumed to be equal to the recovery temperature T _r , given by:

(4) \begin{align}{T_r} = {\rm{\;}}{T_\infty }\left( {1 + r\frac{{\gamma - 1}}{2}M_\infty ^2} \right) \end{align}

Where T _∞ is the free stream static temperature at the given altitude, M _∞ is the free stream Mach number, γ is the specific heat ratio, and ‘r’ is the recovery factor. The recovery factor is given by = Pr ⁿ , n = 0.5 for laminar flow and 1/3 for turbulent flow. The assumption of T _w = T _r holds good for subsonic and supersonic flows; it is conservative for the current study. The earthshine reflection from the bottom surface of the aircraft is estimated as i _s-bot-earth = (1−ɛ _acs ) G _earth , where G _earth is the earth irradiance on the aircraft’s bottom surface. It is estimated using the methodology of Mahulikar et al. [ Reference Mahulikar, Potnuru and Rao30,Reference Mahulikar, Rastogi, Bhatt and Valodhi31]. In the current study the earth’s surface temperature is assumed to be 30^oC and the earth’s emissivity (ɛ _ed ) is taken as 0.95. The transmission from the earth to the aircraft bottom surface is calculated using LOWTRAN 7 [Reference Kneizys, Shettle, Abreu, Chetwynd, Anderson, Gallery, Selby and Clough32]. The sky emission i _sky is given by ɛ _sky e _sky / $\pi$ , where ɛ _sky is the emissivity and e _sky is the blackbody radiation of the sky at the ambient air temperature, for the given altitude. Berger et al. [Reference Berger, Bathiebo, Kieno and Awanou33] have used LOWTRAN and sounding balloon data to provide a relationship of total sky emissivity as a function of altitude. The sky emissivity in the SWIR band and MWIR is approximately 1.0, since the temperature of sky is low, the overall sky emission in the SWIR and MWIR band is insignificant. In the LWIR band, the sky emission is significant but the sky emissivity is well below 1.0, and varies with altitude. At sea level, the sky emissivity in the LWIR band is 0.47 and decreases as the altitude increases, at 4km altitude it is equal to 0.10. The IR signature (contrast) of aircraft is i _s-bot − i _sky, the sky emission reduces the overall IR magnitude. At lower altitudes (1–2km), the sky temperature and sky emissivity (LWIR) are higher compared to the higher altitudes, therefore, sky emission has significant contribution to overall IR signature of the aircraft. At higher altitudes, since the ambient temperature as well the sky emissivity is low, the contribution of sky emission in IR signature (LWIR) is insignificant. For example, at sea level M _∞ = 1, the IR signature due to aircraft surface is 216.36W/m²-sr, the sky emission is 46.44W/m²-sr, and the IR contrast is 169.92W/m²-sr. While, at h = 4km, M _∞ = 1, the IR signature due to aircraft surface is 140.63W/m²-sr, the sky emission is 5.979W/m²-sr, and IR contrast is 134.65W/m²-sr. The IR signature is reduced by 21.4% at sea level, and at h = 4km, it is reduced by 4.125% by the sky emission. The sky emission contribution continues to reduce with increase in altitude.

Using the data from Fig. 4 of Berger et al. [Reference Berger, Bathiebo, Kieno and Awanou33] the spectral data is extracted and linearly extrapolated to the 6km ISA condition. At this altitude, the ɛ _sky in the LWIR band is 0.04. Figure 1 shows the variation of radiation contrast flux intensity of the aircraft bottom surface with M _∞ for the three IR bands. The IR contrast of the aircraft bottom surface increases with M _∞ due to increase in the aircraft surface temperature from aerodynamic heating. When the aircraft emissivity is equal to one, the total IR signature of the aircraft is due to the surface temperature of aircraft alone. When ɛ_acs is 0.5, some part of the aircraft bottom surface radiation is contributed by the earthshine also, and when ɛ_acs is 0, the aircraft bottom surface radiation is due to the earthshine alone. The earthshine does not depend on the M _∞, thus when ɛ_acs is 0, the total IR radiation from aircraft bottom surface will not change with M _∞. From Fig. 1, it is also seen that the IR signature of the aircraft bottom surface is dominant in the LWIR band followed by the MWIR band and negligible in the SWIR band. It is because the aircraft surface temperatures due to aerodynamic heating in the considered range of M _∞ are below 400K. Based on Wien’s displacement law, the IR radiation peaks in the LWIR band at these temperatures. At supersonic Mach numbers, some radiation is seen in the MWIR band, but for the range of Mach numbers under study, the MWIR emission is still lower than the LWIR emission. The temperatures at these Mach numbers are not high enough to radiate in the SWIR band. In the SWIR band the peak radiation occurs in temperature range 966–1,499K.

Figure 1. IR contrast intensity of aircraft surface vs. M _∞ at 6km, ISA, (a) ɛ_acs=1, (b) ɛ_acs= 0.5.

3.0 IR signature of exhaust plume potential core from bottom view

The plume of an aero-engine has a unique structure that resembles an onion peel with various iso-concentrate/isotherm layers. The innermost part of the plume is known as the potential core, which is relatively shorter than the overall length of the plume. The potential core is the region within the plume where there is no mixing of exhaust constituent with the atmosphere. The temperature and molar concentration of CO₂ and H₂O (vap.) are constant and highest in the potential core plume region. The plume potential core is the maximum contributor to the IR signature of the exhaust plume. In this study, the IR signature of the plume potential core is studied and compared with the aircraft surface radiation.

Unlike opaque solid surfaces, plume is a transparent gaseous medium, therefore, the background radiation will also pass through it. The IR contrast intensity of the plume from the bottom view, in a given IR band, can be estimated as i _p-cont = i _p-bot + $\tau$ _plume i _sky − i _sky . The IR intensity due to the plume is given by i _p-bot = i _p-bot-int + i _p-bot-earth , where i _p-bot-int is the IR intensity due to the plume gases and i _p-bot-earth is the reflected earthshine from the plume. Since the molecular dimension of the gaseous molecule is small compared to the wavelength of IR-EM spectrum, scattering, and therefore, the reflectivity of the plume can be assumed to be zero, making i _p-bot-earth zero. Thus, making i _p-bot = i _p-bot-int . However, if soot particles are present in the plume, scattering cannot be neglected. The soot particles emit radiation in all IR wavelengths; thus, changing the IR signature behaviour of the plume. Presence of soot particles has not been considered in this study. The IR intensity from the plume gases can be calculated as:

(5) \begin{align}{i_{p - bot - int}} = {\varepsilon _p}{e_{{b_p}}}/\pi \end{align}

Where ${e_{{b_p}}}$ is black body emissive power of the plume in given wavelength band. Unlike aircraft surface, engine exhaust plume emissivity ( ${\varepsilon _p}$ ) has spectral dependence, ${\varepsilon _p}$ is different in different IR bands. If the hydrocarbon fuel used for combustion is assumed pure and the combustion is complete, then the engine exhaust plume consists of CO₂, H₂O (vap.), O₂, and N₂. The constituents such as CO, NO_x and SO_x can also be present in the plume but their contribution to overall IR signature of plume is negligible [Reference Bhatt and Mahulikar34]. O₂ and N₂ are inert to the IR radiation, while CO₂ and H₂O participates in IR radiation. The emission in different IR bands by the CO₂ and H₂O is dependent on their molar concentration, plume exhaust temperature and the exhaust pressure. In the present study, Gasturb14 [Reference Kurzke and Halliwell35] is used for obtaining data for a turbojet engine. The design point for the engine is assumed sea level static and the data is generated for the off-design conditions, i.e. 6km, ISA for various M _∞. The design point for a fighter aircraft can be different than the sea level static; however, the design point does not affect the trend of engine temperature with Mach number. This may change the magnitude of IR signature at off design points but overall trends will remain the same. Majority of the military turbofan engines use afterburners; wherein additional fuel is burned in the jet pipe of the afterburner to increase the thrust for a shorter duration. Max dry mode (maximum dry mode) is the maximum power of the engine without an afterburner; maximum reheat mode (max reheat mode) is the maximum power of the engine with a full afterburner engaged. In the present study, the IR signature of the exhaust plume is analysed in max dry mode and max reheat mode of the engine. Table 1 shows the engine data generated using Gasturb14. The fuel is considered to be Jet A1, the chemical formula for which is approximately C₁₁H₂₁ [Reference Philippe and Cathonnet36]. The mole fractions of the exhaust plume constituents are estimated by assuming complete combustion [Reference Jackson37]. Table 2 shows the molar fraction of CO₂ and H₂O (vap.) for different M _∞ at 6km, ISA conditions for maximum dry power of engine.

Table 1. Gasturb data for 6km, ISA

Table 2. Molar fraction and transmissivity of engine exhaust constituents, 6km, ISA, max dry

The emissivity of engine exhaust gases can be calculated using the LBL model, band model, or the global models. The LBL model is the most accurate method [Reference Taine38] for estimating the radiation properties of gaseous medium using spectral databases such as HITEMP and HITRAN. In the present study the LBL model is used for estimation of the radiation properties of CO₂ and H₂O using HITRAN 2016 [Reference Gordon39] database. The transmissivity of individual gas molecule is given by: ${\tau _i} = \exp \left( { - {k_i}.{N_i}.L} \right)$ , where τ _i is the transmissivity by the individual gas, k _i is the absorption coefficient of the gas molecule at given pressure and temperature, N _i is the molecular number density given by: $N = \left( {2.6867 \times {{10}^{19}}} \right).\left( {\frac{{273.15}}{T}} \right).\,{P_{mol}}$ , and L is the pathlength in cm. The absorption coefficient (k _i ) is estimated using the molar fraction, exhaust pressure and temperature of the engine exhaust constituents (CO₂ and H₂O) at the nozzle exit. The transmission calculation depends on the line of sight (LOS) or the pathlength (L) through the potential plume core. The shape of potential core for axisymmetric nozzles is approximately like a cone with the base diameter of the engine exhaust. From the bottom view, the pathlength can be conservatively taken equal to exhaust diameter of the nozzle.

The transmissivity of the potential plume core is high in all the IR band for the max dry mode. Plume is almost transparent in LWIR band for both CO₂ and H₂O (Table 2). In the MWIR band transmissivity of the CO₂ decreases with the M _∞, and ranges from 0.98 to 0.96. The H₂O (vap.) does not radiate in MWIR band, it’s transmissivity in the MWIR band ranges 0.997–0.998. Therefore, the total emission in MWIR band is due to CO₂ alone. In the SWIR band, for M _∞ < 1.2, the transmission due to CO₂ is of the order of 0.999; at supersonic speeds (>1.2) the transmissivity is of the order of 0.998. The H₂O transmission in SWIR band is of the order of 0.997. Overall, in the SWIR band, the transmissivity of exhaust plume is very high. For the homogenous gas mixtures, the overall mean transmissivity ( $\overline {\tau \;} $ ) in the given IR band is the product of transmissivity of individual gas constituent, given by: $\overline {\tau \;} = \mathop \prod \nolimits_{i = 1}^n \overline {{\tau _i}} $ . Figure 2 shows the variation of plume transmissivity in MWIR with M _∞. The transmissivity decreases with M _∞.

Table 3. Emissivity of plume potential core, 6km, ISA, max dry and max reheat

Figure 2. Variation of CO₂ transmissivity in MWIR band with M _∞, 6km ISA, max dry.

The emissivity of the plume is calculated by assuming reflection as zero, therefore, mean emissivity ( $\bar \varepsilon $ ) in the given IR band is equal to $1 - \overline {\tau \;} $ . The mean emissivity of the potential plume core in different IR bands for 6km altitude is given in Table 3. The emissivity of the plume is maximum in the MWIR band, followed by the SWIR band, and minimum in the LWIR band. With an increase in M _∞, the thrust requirement of the engine increases, leading to increased pressure and temperature of the plume. The IR signature of the plume is dependent on temperature and emissivity. The plume emissivity is dependent on, temperature, pressure and molar fraction of the IR participating gases (CO₂ and H₂O). With an increase in pressure and the temperature of the exhaust gases, the emissivity of CO₂ and H₂O increases due to collision broadening. Collision broadening is the broadening of spectral lines due to increased collisions between the molecules of IR participating gas (e.g. CO₂ and H₂O). Increased pressure leads to higher density of molecules in the plume, resulting in an increase in the frequency of collisions between molecules. Higher temperature increases the mean kinetic energies of the gaseous molecules leading to high frequency of collision. Thus, increase in pressure and temperature leads to increase in plume emissivity due to collision broadening. Although the fuel flow rate increases with an increase in M _∞, the molar fraction of CO₂ and H₂O decreases slightly (in the maximum dry mode of the engine), it is because, the increase in fuel flow rate is lesser compared to the increase in the air mass flow rate to the engine (Tables 1 and 3). For example, from Mach number 0.2 to 0.4, the increase in fuel flow is by 5.63%, but the increase in air flow rate is by 6.21%. The decrease in molar fraction has the effect of decreasing emissivity. As the Mach number (M _∞) increases, the emissivity of the plume rises due to the collision broadening of CO₂ and H₂O molecules. In the maximum afterburner mode, nearly all available oxygen is consumed to burn the additional fuel, leading to a higher molar fraction of CO₂ and H₂O. However, in the afterburning mode, the molar fraction of CO₂ and H₂O shows negligible change with increase in the Mach number. When the engine shifts from maximum dry mode to maximum reheat mode at a given M _∞, emission and absorption increase because of the rise in temperature, pressure, and the concentration of CO₂ and H₂O.

The IR contrast of the plume is be given by i _p-cont = i _p-bot + τ _plume i _sky − i _sky. As seen from Tables 2 and 3, plume is transparent in the LWIR band, transmission in the SWIR band is close to 0.99 In the MWIR band, it ranges from 0.96 to 0.98. Since the sky emission is negligible in the SWIR and MWIR band, τ _plume i _sky − i _sky is approximately equal to zero in all three IR bands. Thus, the IR contrast of the plume can be given by i _p-cont = i _p-bot . The IR contrast of the plume is approximately equal to the self-emission from the plume in all three IR bands. Figure 3(a) shows the variation of IR intensity of the plume from the bottom view in three IR bands for maximum dry mode of the engine. The IR intensity of the plume is maximum in the MWIR band followed by the SWIR band and negligible in the LWIR band. In the MWIR band CO₂ is the only emitter, in the SWIR band both CO₂ and H₂O emits the radiation, but the overall emission in MWIR is 30–37 times more than in SWIR band. The IR intensity increases with M _∞ because of two effects (1) rise in the exhaust gas temperature, and (2) increases in the plume emissivity both in SWIR and MWIR band. The emission of both CO₂ and H₂O is negligible in LWIR band.

Figure 3. Variation IR intensity of the plume with M _∞, 6km, ISA, (a) Max Dry, b) max reheat.

In the reheat mode of the engine, the fuel flow rate, and the exhaust gas temperature increase significantly compared to the max dry mode. Figure 3(b) shows the variation of plume IR emission for max reheat mode of the engine, when seen from below for 6km ISA conditions. The plume emission in max reheat mode is significantly high compared to the max dry mode. For the MWIR band the rise is almost 16 times, 66 times for the SWIR band and 25 times for the LWIR band. The high emission is mainly due to the high exhaust gas temperature, which is almost doubled. For M _∞ = 1.8, the temperature rise is approx. 2.09 times, and the emissivity has increased by 21 % in MWIR band. The increase in IR signature is more pronounced in the SWIR band compared to the MWIR. At M _∞ =1.8, the ratio of MWIR to SWIR radiation is 8.16 in max reheat mode, compared to 30 in the max dry mode. This difference is due to the rise in exhaust gas temperatures, which increase from 1,467K in max dry mode to 1,526K in the max reheat mode. The peak radiation for these temperatures occurs at wavelengths of 1.97 and 1.89μm, respectively, which is near to the SWIR band. Although the radiation in max reheat mode peaks in the SWIR band, the overall IR radiation of the plume is lower in SWIR compared to the MWIR band. This is because: (1) The emissivity of the plume is lower in the SWIR band and (2) the SWIR band has a narrower bandwidth compared to the MWIR band. Table 3 shows the comparison of exhaust gas temperature and emissivity for max dry and max reheat mode of the engine.

Figure 4 shows the variation of IR intensity of plume’s potential core with altitude from direct bottom view at M _∞ = 1. The IR intensity is negligible across all altitudes in the LWIR band. In the SWIR band, the plume’s IR intensity is very low, and it decreases further with the altitude. Similarly, in the MWIR band, the IR intensity decreases continuously with increase in the altitude. This is because, as the aircraft gains the altitude at a constant M _∞, the thrust requirement of engine reduces, leading to reduction in exit pressure and temperature. The lower temperature causes a direct decrease in the radiation intensity. Additionally, the reduction in pressure, temperature and the molar fraction of CO₂, H₂O leads to decrease in the emissivity of the exhaust plume in all the three IR bands. Consequently, the overall IR intensity of the plume’s potential core decreases with increasing altitude at a constant M _∞.

Figure 4. Variation of plume IR intensity flux with altitude, M _∞ = 1, ISA, max dry.

4.0 Comparison of aircraft surface and plume potential core radiation from bottom view

The radiation characteristics of the aircraft surface and exhaust plume differ significantly. The aircraft surface radiates in all the IR wavelengths; while the plume is a select band emitter, radiating predominantly in specific IR bands. The aircraft external surface temperature, caused by the aerodynamic heating, is comparatively lower than the engine exhaust temperature. The peak radiation from the aircraft external surface occurs in the LWIR band, while the peak radiation of the engine plume occurs in the MWIR band for max dry mode and in the SWIR band for max reheat mode. For example, the maximum adiabatic wall temperature (recovery temperature) of the aircraft bottom surface for M _∞ = 1.8 at 6km altitude is 395K, while the exhaust gas temperature in the max dry mode is of the order of 795K. Thus, the peak radiation wavelength of the aircraft surface is 7.33µm, while the plume peak radiation occurs at 3.64μm. In the max reheat mode, the plume emission peaks near the SWIR band. For example, at M _∞ = 1.8 at 6km altitude, the exhaust gas temperature is approximately 1,526K, which corresponds to peak emission wavelength of 1.89µm.

From Figs 1 and 3, it is evident that the aircraft surface radiation is important in the LWIR band, while the plume radiation is prominent in the MWIR band. However, when the aircraft is flying at supersonic speed, the aircraft surface temperature is high enough to emit in the MWIR band. Figure 5 presents the variation of plume to surface radiation ratio with M _∞ in three IR bands. The plume /surface IR is referred as ‘radiation ratio’ henceforth in this document. The emissivity of the aircraft bottom surface (ɛ _acs ) is considered to be 1 for the comparison. When ɛ _acs is 1.0, the surface radiation is maximum for a given temperature. A decrease in emissivity reduces the radiation intensity, affecting the magnitude and the radiation ratio, but the overall trend remains unchanged. The radiation ratio in MWIR band decreases with M _∞ (Fig. 5a), because, the aircraft surface temperature increases with increase in M _∞. At high M _∞, surface temperatures are high enough to emit in the MWIR band. The MWIR radiation ratio trend with M _∞ is similar for both maximum dry and reheat mode of the engine. At low Mach numbers, the plume signature is significantly higher than the surface IR signature. At M _∞ = 0.3, the MWIR radiation ratio is of the order of 289 for max dry mode and 4,891 for max reheat mode. At M _∞ = 1.8, the MWIR radiation ratio is 2.2 for max dry mode and 45.9 for max reheat mode. Normally fighter aircraft do not fly at speeds higher than M _∞ = 2, therefore, for a fighter aircraft, potential plume core IR signature is always higher than the surface IR signature in the MWIR band.

Figure 5. Comparison of plume and aircraft surface emission from direct bottom view, 6km ISA, ɛ_acs =1, (a) MWIR, (b) LWIR.

Figure 5(b) illustrates how the radiation ratio varies with M _∞ in the LWIR band. Although the plume temperature is higher compared to the aircraft bottom surface, the emissivity of the plume potential core is negligible in LWIR band. The plume potential core is almost transparent in the LWIR band, and the emission is negligible in both max dry and max reheat mode. The LWIR radiation ratio is of the order of 10^-3 for the max dry mode and 10^-1 for the max reheat mode. Since the SWIR signature of the aircraft surface and the potential plume core is negligible for the max dry mode, it is not plotted in Fig. 5. However, in the max reheat mode, the SWIR signature of the plume’s potential plume core becomes significant.

The above comparison of the plume and aircraft bottom surface is carried out for a single band IR sensor. Nowadays, IR sensors have the capability to detect the IR radiation in two different IR bands. Dual band sensor can be a combination of SWIR, MWIR and LWIR band. The dual-band capability offers better target identification and reduces false alarms compared to a single band sensor. The plume is a major emitter in the MWIR band followed by SWIR band, and negligible in LWIR. If soot particles are present in the plume, they emit in all the IR bands. Conversely the aircraft bottom surface is a major emitter in the LWIR band followed by MWIR band, and negligible in SWIR. When a dual-band (MWIR-LWIR) or (SWIR-LWIR) seeker observes an aircraft from a direct bottom view, it always has an option to lock onto to either the plume or the aircraft surface.

Figure 6(a) shows the variation of the ratio of potential plume core IR signature in MWIR band to aircraft surface IR signature in LWIR for ɛ _acs = 1. The radiation ratio (MWIR/LWIR) continuously decreases with M _∞. The trend is similar for both max dry and max reheat mode, and differ only in the magnitude. In max dry mode, the plume MWIR signature is higher than the aircraft bottom surface LWIR signature up to M _∞. = 1.1. Above M _∞ = 1.1, the surface’s LWIR signature surpasses the plume’s MWIR signature. This critical Mach number at which the surface LWIR signature surpasses the plume MWIR signature depends on aircraft surface emissivity, engine power and altitude. The IR signature received by the sensor located away from the aircraft is further attenuated by the atmosphere. The atmospheric transmission in the LWIR band is higher compared to the MWIR band, therefore, the net irradiance received by the sensor decides the band to be used for the lock on. The atmospheric transmission between the aircraft at 6km and the sensor on the ground is calculated using LOWTRAN, the τ _sky in the MWIR band is 0.56 and τ _sky in the LWIR is 0.85.

Figure 6. Variation of ratio of plume (MWIR) to aircraft (LWIR) surface radiation, 6km with M _∞, ISA, ɛ_acs =1, (a) from the aircraft (b) received by the sensor.

Figure 6(b) shows the ratio of the irradiation flux (W/m²-sr) received by the sensor located on the ground (for ɛ_acs=1). In the max dry mode, the LWIR irradiance of the aircraft surface received by the sensor is higher than the plume MWIR irradiance. However, in the max reheat mode, the plume MWIR irradiance received by the sensor is always higher than the aircraft bottom surface LWIR irradiance. Therefore, from the bottom view, the LWIR band is more suitable for the lock on compared to the MWIR band in the max dry mode. In the max reheat mode, MWIR band is more suitable than the LWIR band. Normally aircraft operates in the max dry mode; max reheat is occasionally used by the aircraft (for faster climb/acceleration or during a manoeuvre). Thus, from the bottom view of the aircraft, the aircraft surface IR signature in the LWIR band becomes more important than the plume’s potential core IR signature in the MWIR band. As the sensor approaches the aircraft, the atmospheric transmission increases in both LWIR and MWIR bands (Fig. 7), thus the choice of lock-on between plume and surface may further change. The atmospheric transmission in the LWIR band is higher than the MWIR band.

Figure 7. Variation of atmospheric transmission with altitude.

The plume’s potential core IR signature in max reheat mode is significantly higher than the surface radiation; thus, max reheat mode should be avoided when entering or flying over a SAM zone. If the dual-band sensor operates in the SWIR and LWIR bands, the SWIR band is not effective in detecting plume radiation in the max dry mode. However, in max reheat mode, the plume signature becomes significant in the SWIR band as well. Figure 8 shows the variation of the ratio of potential plume core SWIR radiation to aircraft surface LWIR radiation. The plume potential core SWIR band signature is always higher than the aircraft surface LWIR signature for almost all M _∞. At M _∞ = 1.8 the radiation ratio (SWIR/LWIR) is less than 1.0. In max reheat mode, both the plume MWIR and SWIR band signatures are higher than the aircraft external surface LWIR signature. Thus, max reheat mode should always be avoided when approaching a SAM site.

Figure 8. Variation of ratio of plume (SWIR) to aircraft (LWIR) surface radiation, 6km with M _∞, ISA, ɛ_acs =1, max reheat.

The plume MWIR to aircraft external surface LWIR radiation ratio depends on the aircraft surface emissivity. Figure 9 illustrates it for different ɛ _acs (for the max dry mode). It can be observed that for ɛ _acs = 1.0 and 0.5, the plume potential core MWIR signature is higher than the aircraft bottom surface LWIR signature at subsonic M _∞. The radiation ratio (MWIR/LWIR) decreases with increase in M _∞. When ɛ _acs ≤ 0.2, the plume radiation is nearly equal to the surface radiation at low M _∞, but becomes higher than the surface radiation as the M _∞ increases. This is because the aircraft surface radiance is a combination of skin emission and earthshine. At low M _∞, the skin emission is very low due to low surface emissivity and lower surface temperatures, but the earthshine reflection is high due to high reflectivity (ρ _acs = 1− ɛ _acs ) of the aircraft surface. The earthshine reflection is calculated assuming an earth surface temperature of 30^oC, and the aircraft surface self emission is calculated using recovery temperature at 6km altitude. When ɛ _acs ≤ 0.2, the ratio (plume MWIR to surface LWIR) increases with increase in the M _∞. It reaches its peak at a specific M _∞ and then decreases. This is because, for ɛ _acs ≤ 0.2, as M _∞ increases, the plume emission also increases, and the contribution of the aircraft surface self emission is significantly less compared to the earthshine reflection. The earthshine component is independent of M _∞. As a result, the radiation ratio (MWIR/LWIR) continuously increases until a certain M _∞, at which the skin-emission component starts to contribute, causing the radiation ratio (MWIR/LWIR) to decrease (Fig. 9).

Figure 9. Variation of ratio of plume (MWIR) to aircraft surface (LWIR) radiation, with M _∞ for different ɛ_acs.

The dual-band sensor can be a combination of any two out of the SWIR, MWIR and the LWIR band. The plume and aircraft hot surface emission is seen in the MWIR and the SWIR band; the only difference is that the plume emission is more prominent in the MWIR band. At high speed, aerodynamically heated surfaces also emit in the MWIR band. Thus, having SWIR-MWIR as a dual-band sensor does not provide any additional advantage for aircraft detection. Combining the LWIR band with the SWIR or MWIR band provides the advantage that the aircraft surface heated due to aerodynamic heating can also be identified in addition to the hot engine components and exhaust plume. The plume SWIR emission is very low in the max dry mode compared to the MWIR emission; the SWIR plume emission is significant only in the max reheat mode. Out of the three combinations of dual IR bands, the MWIR-LWIR combination will be able to detect the plume from the max dry mode to the reheat mode of the engine. If the plume is shielded by the aircraft from the frontal view, the LWIR band will be able to detect the aircraft surfaces from the frontal aspect. Overall, over the wider range of aircraft speed and engine power, the MWIR-LWIR dual band combination is best suited to identify and ascertain the target. The MWIR-LWIR dual band is providing all aspects and all-weather capability to the missile.

The position of the sensor relative to the aircraft, along with its characteristics such as the signal-to-noise ratio (S/N) and the noise equivalent irradiance (NEI), play a significant role in determining the detection range of the aircraft. If other parameters of sensor are constant, smaller the NEI, larger is the detection range of the target. The sensing technology of the MWIR band is completely different than the LWIR band. The MWIR camera detectors use indium antimonide (InSb), lead selenide (PbSb), or mercury cadmium telluride (HgCdTe) to sense thermal emissions. Since the sensing technology of the MWIR and the LWIR sensors is different, their respective noise equivalent irradiance (NEI) values may also be different. Therefore, the lock-on range should be studied on the basis of specific characteristics of each sensor. Also, once the missile/sensor starts chasing the target, the atmospheric attenuation continuously changes the IR signature received by the missile. From the point of view of a hit leading to a kill, it is always beneficial to lock on to the aircraft surface towards the terminal guidance of the missile. If a missile directly hits the aircraft surface, it will cause greater damage to the aircraft. However, if the missile detonates near the plume, the explosion could cause minimal harm since the length of the plume can be equivalent to or greater than that of the aircraft. Since the LWIR band can detect the aircraft surfaces, in a dual-band IR detector or missile, the LWIR band will always provide an advantage for the terminal guidance of the missile.

5.0 Conclusion

• • In the MWIR band, the ratio of plume to surface IR radiation decreases as M _∞. increases. At low M _∞., the potential core radiation is higher than the surface radiation. However, for M _∞.> 1, the surface radiation also contributes significantly to the IR signature of the aircraft, eventually becoming comparable to the plume radiation at higher supersonic M _∞.

• • In the LWIR band, surface radiation is significantly higher than the plume radiation. Plume potential core is transparent to IR radiation in the LWIR band in max dry as well as max reheat mode.

• • When ɛ_acs = 1, in the max dry mode, the plume MWIR emission at low M _∞ is higher than the surface LWIR emission. As the M _∞ increases, the plume MWIR to surface LWIR emission ratio decreases. At supersonic Mach numbers, the surface LWIR radiation is higher than the plume MWIR radiation. When ɛ_acs < 0.5, the plume MWIR emission is higher than the surface LWIR radiation for all M _∞.

• • In the max reheat mode (ɛ_acs = 0.5), the plume MWIR as well as SWIR emission is higher than surface LWIR emission for all range of M _∞ under study.

• • When the aircraft surface emissivity is unity, the plume MWIR radiation is higher than the surface LWIR radiation for subsonic M _∞. However, sensor located 6km directly below the aircraft receives higher radiation from the surface (in max dry mode). It is because, the atmospheric attenuation is higher in the MWIR band compared to the LWIR band.

• • In the max reheat mode, the plume MWIR radiation is significantly higher than the surface LWIR emission. Despite high absorption through the atmosphere, the MWIR emission from the plume received by the sensor positioned 6km directly below the aircraft, exceeds the LWIR radiation.

• • The MWIR-LWIR dual band combination is the best suited combination for a dual band IR sensor/detector for aircraft application. It enables sensor to view aircraft as well as the exhaust plume for a range of Mach number and engine power. The combination provides all-aspect all-weather capability to the detector.