It is conventional wisdom in the publishing industry that, despite the old adage, readers do indeed judge books by their covers. So, it seems, do passengers on the No. 29 bus. For a middle-aged man reading Clare Mulley’s The Women Who Flew for Hitler, some of the looks I got made me so uncomfortable that I took to hiding the cover behind a newspaper.

So let’s get one thing straight from the beginning: this is not a niche book for Third Reich enthusiasts, nor a seedy excuse to fantasise about women in Nazi uniforms. Do not be put off by the awful title: it is in fact a serious double biography of two of the most remarkable women in the history of aviation.

The first of Mulley’s subjects, and the more famous of the two, is Hanna Reitsch. Reitsch was the darling of the prewar German press and one of the most giftedfliers of her generation. At the age of 21, this extraordinary woman flew a glider through storm clouds to set a new world altitude record for unpowered flight. In 1937 she became the first woman ever to fly a helicopter, and during the second world war she flew every plane going, including manned versions of the V-1 flying bomb.

Her physical courage seemed to know no bounds. In 1942, she crashed in a jet plane prototype she was testing; but despite breaking her back in several places, and having her nose torn from her face, she was back flying again within a year. She was the first German woman to be made a Flight Captain, the first to receive the Military Flying Medal, and the first to receive the Iron Cross, First Class. ‘She was the one and only Hanna Reitsch,’ as one of her male colleagues put it, ‘a symbol of German womanhood and the idol of German aviation.’

The second woman in Mulley’s book, though less well known, is perhaps even more impressive. Melitta Schiller was a military test pilot whose determination to stress her planes to their very limits seemed almost suicidal. According to one contemporary, taking a plane into even a moderate nosedive was ‘something many male pilots already regarded as an act of heroism’. Melitta insisted on flying her planes almost vertically towards the ground, only pulling out at the very last moment. On one such dive the canopy of her plane blew off, leaving her exposed to the elements as she tried to bring her plane back under control. On another occasion her windscreen exploded. She was forced to crash-land several times, and once had to bail out when her plane caught fire. Yet she remained undeterred: during the course of her career she completed more than 2,000 nosedives in the name of research.

The half-Jewish Melitta Schiller, who supported the plot to kill Hitler.

However, what made Melitta Schiller so exceptional was that the equipment she was testing during these dives was often also designed by her. The research of this talented aeronautical engineer gave rise to scores of innovations, especially in night-fighter technology. Thus, not only did she become the second woman to be awarded the Iron Cross, First Class, but towards the end of the war she was also appointed head of her own research station. She would spend her mornings performing death-defying manoeuvres in the air and her afternoons at the drawing board, perfecting her designs.

As a story of two women bursting through the very low glass ceilings of their time and rising to the pinnacle of their profession, Mulley’s book is a satisfying, rollicking read. But there is a great deal more nuance here than first meets the eye. Neither woman regarded herself as a feminist — indeed, Melitta openly repudiated the very idea. Both worked in the service of a vile regime, and were well aware of the crimes it was committing. One wants to celebrate their achievements, but Mulley deliberately makes us uncomfortable about doing so.

Furthermore, she reveals that despite some superficial similarities, these were two very different women. Hanna was brash, impatient for change, and became a fanatical Nazi. She had private dinners with Göring, Himmler and Hitler, and even spent time with Hitler in his bunker during the final days of the Nazi Reich. She survived the war but kept the taint of her Nazi past until her death in 1979.

Melitta, by contrast, lived by the traditional values of the old German Junker class. She was also half-Jewish, and was only spared deportation to the camps because her pioneering work was worth too much to the regime. Before the war she married into the family of Claus von Stauffenberg, and wholeheartedly supported his plot to kill Hitler in 1944. She died in a doomed attempt to find her husband at the very end of the war when her plane was shot down by the Allies. Each woman in her way was therefore emblematic of a different facet of German society during the most turbulent years of the 20th century.

Mulley’s biography is well researched, beautifully written, and gives a perspective on the war that even seasoned students will find refreshing. So do not be put off by the title: this is one book that should not be judged by its cover.