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Assessing the impact of an academic paper on other academics can be done (with its pros and cons) using the number of citations the paper attracts. For more detailed information on how the paper influenced the citing work, one can read the citing paper, visit the authors' webpages and even email them. All of this is made possible by the fact that most (successful) academic works result in the public, searchable, dissemination of that work.

However, how can I assess the impact a paper has on industry? Industrial work, which results in products rather than papers, will usually not leave an easily identifiable trail connecting it to the previous work on which it builds up. But funding agencies put emphasis on reutilisation of academic results for industrial applications. Recently, we got a consulting job because a semiconductors company came by a paper I wrote a couple of years ago and decided to hire us to advise them on how to build their production process. In my next application for research funding I can use this contract to exemplify how my research is useful for industry. But what about all the other companies that are using our results and we don't know about? Is there a way to estimate this impact?

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    Start by making a list of all the industries that could use your paper... – Solar Mike May 6 '18 at 11:08
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This answer deals primarily with engineering products, I'm not sure if it applies to say, the software industry. Most research papers will present some results, but not industry-ready solutions. Most industries will not have full fledged research teams to scan scientific literature and work on translating it into products. So there is a gap that an interested industry needs you to bridge. Therefore, when an industry finds something interesting, they will contact you, as has already happened with you. The chances of many companies using your research without your knowledge is slim.

If you are interested in application-oriented research, you can increase the chances of this happening by attending certain conferences which have industry delegates, and proactively interacting with them. This can lead to collaborations, sponsored projects and a general understanding of their requirements. As you said, there is not much of a public paper trail, so human interaction is the only way.

To know what impact other people's research has on industry, you could search for papers sponsored by those particular industries (acknowledgement section for example).

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Count of number of times your paper has been downloaded would be a valuable metric.

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