This works for my rails application - sinatra should not be any diffrerent. Just change the path to your ruby binaries...
EnvironmentVariables for HOME/HOMEDRIVE/HOMEPATH are necessery on a windows server environment using Active Directory users. You can ignore this on a single local machine.
<?xml version="1.0" encoding="UTF-8"?>
<configuration>
<system.webServer>
<handlers>
<add name="httpplatformhandler" path="*" verb="*" modules="httpPlatformHandler" resourceType="Unspecified" requireAccess="Script" />
</handlers>
<httpPlatform stdoutLogEnabled="true" processesPerApplication="1" stdoutLogFile="C:\inetpub\wwwroot\rails\FrontEndServer\log\rails.log" startupTimeLimit="20" processPath="C:\RailsInstaller\Ruby2.3.0\bin\ruby.exe"
arguments=""C:\RailsInstaller\Ruby2.3.0\bin\puma" --env production --dir "C:\inetpub\wwwroot\rails\FrontEndServer" -p %HTTP_PLATFORM_PORT% ">
<environmentVariables>
<environmentVariable name="HOME" value="C:\temp"/>
<environmentVariable name="HOMEDRIVE" value="C:\temp"/>
<environmentVariable name="HOMEPATH" value="C:\temp"/>
</environmentVariables>
</httpPlatform>
</system.webServer>
</configuration>