# Can stainless steel replace titanium for Mach 3+ speeds?

In the documentary Wings of Russia: MiG-25 and MiG-31, they mentioned both aircraft had to use special stainless steel alloys and arc welding to withstand the Mach 2.83 - 3.2 speeds.

I couldn't help but recall the space pen vs. pencil myth. Could the SR-71 (Mach 3.3) have been built using such stainless steel alloys instead of covertly importing the titanium from Russia?

The major supplier of the ore was the USSR. Working through Third World countries and bogus operations, they were able to get the rutile ore shipped to the United States to build the SR-71.

Since the SR-71 flew higher, I'd guess both had comparable EAS / dynamic pressures. The titanium used on the SR-71 was an alloy, figuring out which alloy to use and how to shape it caused many challenges.

So gained knowledge and cool factor aside, what other factors are there?

• Stainless steel is about 2 times as dense as titanium so for the same size, it would be heavier which means more fuel burn to get to Mach 3+. Oct 7 '16 at 20:42
• I'm going to relay a couple things I read about, but not make an answer because I don't want to spend the time researching the information: 1. Titanium is extremely expensive and difficult to work. Where the US just used Titanium wholesale, the Russians only used it where it was specifically needed. 2. A Russian jet once made a run over Egypt at speeds greater than Mach 3. What was not understood at the time was that flying at that speed destroyed both engines and they were replaced. Oct 10 '16 at 0:09

Both the MiG-25 and MiG-31 designs had engines that would overheat and be damaged an anything past Mach 2.83, so both planes were limited by this. Typical speeds were closer to Mach 2.5 to extend the life of the planes. The highest aerodynamic heating occurs at the leading edges. It's possible that the MiG designs used titanium in these areas but opted for steel in most other areas, which was cheaper and easier to work with. This would have allowed the aircraft to reach speeds closer to the SR-71, even if the engines couldn't keep up.

The SR-71 was designed to cruise at up to Mach 3.3 at 80000ft, a similar altitude to the MiGs. Atmospheric heating is related to the cube of the speed. Mach 3.3 generates 10% more heat than Mach 3.2, and the SR-71 reached at least Mach 3.5. It seems the SR-71 flew faster and higher than the MiGs.

Heat is only one consideration though. Another big issue is weight. Steel is generally much heavier than a comparable structure made from titanium. The SR-71 empty weight was about 40% higher than the MiG-31, but the MTOW was 70% higher. This allows much more payload for mission equipment, but also fuel. The MiGs were designed to fly relatively short range interception or reconnaissance missions, having unrefueled ranges of 2000km or less. The MiG-31 could fly 3000km but only with drop tanks. The SR-71 was designed as a long range reconnaissance aircraft, and had a range of 5400km which enabled it to fly long missions over enemy territory.

Another consideration is size. The SR-71 was a larger plane than either the MiG-25 or MiG-31. It had a wingspan of 17m, compared to 14m of the MiGs, and a length of 33m, compared to 20m and 23m for the MiGs. This means higher forces on the aircraft structure.

Let's note some properties of steel and titanium. For steel, we choose 4340 alloy (oil-quenched and tempered); for titanium, we use the Ti-6Al-4V alloy (solution heat-treated and aged). These are not the 'default treatments' for either material, but put them both in a good light. Note that for titanium, the difference between low-grade and high-grade is not quite as significant as it is for steel.

                     | Steel  Titanium
------------------------------------------
Density:             | 7.85   4.43   g/cm3
E-modulus:           | 200    119    GPa
Yield strength:      | 1520   1103   Mpa
Thermal expansion:   | 12.3   8.6    10^-6 K^-1
Thermal conductivity | 44.5   6.7    W/mK
Cost                 | 3.60+  66-154 USD/kg


Data taken from Callister & Rethwisch, "Material Science and Engineering", 2011, and matweb.

First, it is immediately clear why one would consider replacing titanium; it's mindbogglingly expensive. But is the alternative any good?

Let's look at what stresses heating could induce. We consider for simplicity a uniform rod clamped at both ends, heated up by a temperature difference $\Delta T$. The stress resulting from this temperature differential $\sigma = E\alpha_l\Delta T$ with $\alpha_l$ the thermal expansion coefficient. We rewrite for maximum allowable $\Delta T$ by equating $\sigma$ to the yield strength, $\sigma_y$. $$\Delta T_{max}=\max{\dfrac{\sigma_y}{E\alpha_l}}$$

Thanks to the low thermal expansion, Titanium is a clear winner here, with almost twice the maximum allowable temperature difference, at 1078 kelvin difference versus 618. Note however that steel does have a significantly higher thermal conductivity, so it may be able to transport heat away more efficiently (at the cost of things becoming hot where you don't want this...).

Of course, for various other parts, different guidelines exist; in simple tension loading, we could want to maximize ${\sigma_y}/{\rho}$ with $\rho$ the density (titanium is ~25% better than steel); in compression we could want ${\sqrt{E}}/{\rho}$ if we consider buckling (titanium ~35% better than steel). The key point here however is that none of them make a good match towards titanium, especially if we consider steel that is simply annealed or rolled rather than having special treatments. This is mostly due to its low density. Since making a plane fly at Mach 3 is quite an engineering challenge, the price-tag of the materials may be a lesser issue, and just making a feasible design given any material is quite the challenge.

The bottom line however is that everything is impossible until someone makes it, but until there is a very good incentive to make a supersonic aircraft from steel, it's not going to happen.

• So, the way I read that, your answer is "yes it can", but it would have taken about the same number of engineering leaps to have made the SR71 out of stainless as it did out of titanium. Plus, instead of having a mean looking Blackbird, we'd have had a shiny DeLorean 20 years early. ;) Oct 13 '16 at 18:54
• @Freeman if you mean, the same number of steps in addition to the number in the original design, then, yes. But it might not be possible at all - there will be a fundamental limit where you cannot get past with a steel aircraft, just like you can't build a Mach 2 jet from wood (probably... Spruce Falcon, anyone?). Side note: stainless steel is worse than high grade steel, so your plane will be fast but rusty :) Oct 14 '16 at 8:12
• "there will be a fundamental limit where you cannot get past with a steel aircraft..." ...unless you have very very good active cooling. May 4 '18 at 21:55
• @Sean there will be a temperature where you can't sustain cooling even if you involve cryogenic liquids. Heat transfer does not go to infinity for low temperature sinks (the power to create such a low temperature sink does, though) May 4 '18 at 21:59

There has been a supersonic aircraft made from steel, the XB-70 Valkyrie, up there with the SR-71 in the exclusive club of awesomest planes. It was made of stainless steel/honeycomb (with a bit of titanium structure thrown in).

Take the strongest steel, strongest aluminium and strongest titanium and compare their strength-to-weight ratio. You will find that steel is 3 times heavier than aluminium, but also 3 times stronger: they have the same strength-to-weight ratio, which turns out to be the same ratio for titanium as well. Titanium is the most difficult to make into any desired shape at all, while stainless steel is a well known, benign pet: easy to weld, no fatigue problems if stresses are kept below the fatigue level etc.

So with equal strength-to-weight ratio's, you could make a steel structure that is as light as an aluminium one. That is, if the structure is loaded in tension, like a pressure vessel - which is what the fuselage actually is. With a metal sheet loaded in compression (the upper skin of a wing for instance) the sheet buckles before it reaches the yield strength: only thicker sheets help there, not stronger sheets. That is why aluminium wins when making the average holiday jet aircraft.

• Isn't resistance to buckling a large part of the reason for using a honeycomb structure? As for instance a corrugated cardboard box vs one made of flat sheets of the same weight? May 30 '17 at 4:38
• Yes indeed amd that's how it was done at North American for the XB-70. More expensive than an aluminium sheet though. May 30 '17 at 5:50
• @jamesqf yes, to get the same strength with a solid structure would have required a far greater mass of steel, making the aircraft incapable of flight (and probably so heavy it'd collapse under its own weight). May 30 '17 at 6:07
• Titanium has the very helpful characteristic of superplasticity, so in my humble opinion, shaping it simply requires different methods than steel. Also, for a meaningful comparison, you need to look at the strength at elevated temperatures - room temperature comparisons don't count for much in Mach 3+ designs. May 30 '17 at 7:08
• Thicker plates are not the only way to prevent buckling - honeycomb sandwich structures (like you mention yourself!) and stringers do the job way better than thicker plates. Not sure why you would say that "only thicker sheets help there". And honeycomb material is not that expensive. May 30 '17 at 8:38